I've lived here for two years and visited alone for five weeks prior to living here so I'll shed some light.
1) DEFINITELY get a rail pass to cover your entire trip. It is absolutely worth it. When I came I rode over $4000 worth of trains for under $1000 (I had a three week pass and a two week pass). Just know though--the rail pass covers Japan Rail (JR) lines only--subways are not covered so you will have to buy a ticket for those.
Tokyo:
Getting around:
The Yamanote loop line and Chuo line will almost certainly get you almost everywhere you want for the most part.
Districts to see:
Shibuya, Shinjuku, Ginza, Shinbashi, Minato-ku/Odaiba, Harajuku, Asakusa.
Places to stay:
Its kind of hard to go wrong, really. The last time I was there we stayed at The B hotel in Akasaka. Want to see young, affluent, stunning Japanese women at their classiest? Go there. It's just a very, very pretty part of Tokyo.
Anywhere in Japan you can find a Toyoko in hotel will be a cheap winner with free internet in the room (usually you have to pay extra for internet).
The first night I was in Tokyo I stayed at the Cerulean Tower Tokyu (yes Tokyu not Tokyo) right in the heart of Shibuya, and looked down over Shibuya crossing on a Friday night at 7 PM at dusk from the panoramic bathroom window from the 24th floor. Expensive, but worth every penny and was the most amazing first impression of the world's biggest city to a kid who'd never been on an airplane prior to that morning. The skyline truly was endless in all directions from both the bathroom and main room panoramic windows.
Things to see:
It really is impossible to list them all so here's just a few of my favorites.
--RAINBOW BRIDGE!! Going over to Odaiba (man made island in Tokyo Bay), and sitting down by the water looking out across the bay with the gorgeous bridge back to the mainland with Tokyo Tower in the background is absolutely
stunning.
This is my favorite place in Tokyo, and thus--my favorite place in the entire world. Right there, on the water with the Rainbow bridge.
Go at night. You need to take the Yurikamome, which is not covered by the rail pass (it's not an expensive ticket, it's just hard to realize it's not a JR line for a newbie--I didn't know what to do since I thought it was covered under the rail pass but there was nobody to show my pass to so I blew threw the gates and embarassingly got caught and directed to the ticket machine).
--Shibuya crossing (Hachiko crossing) as has been mentioned. Go at night. I believe Shibuya station's West exit is what will put you right in the middle of it, though Shibuya station was undergoing expansion last time I was there during Xmas 2008 so I'm no longer sure. I also second the Shibuya 109 building in Shibuya crossing to see hotter women than you've ever seen in your life.
--Kabuki-cho in Shinjuku, not far from Shinjuku station. Shinjuku station is also the busiest train station in the entire world. You will see some extremely interesting characters there. Don't take pictures of the people. Kabuki-cho has over 1000 registered yakuza living there (Japanese mafia) and is filled with funky love hotels, soap lands, hostess bars, host bars, kyabakura, you name it anything and everything "mizu shobai" is there. While you could consider it the most dangerous part of Japan, overall it is still safe, and the yakuza have far better things to do than bother some wanker tourist so don't worry, nobody there will care about you. Go at night on a weekend to really see stuff.
--Just wander around Shibuya/Shinjuku, you'll see and find and hear amazing things. The opening scene from Lost in Translation where Bill Murray is in the cab and wakes up to the endless road of lights is in Shinjuku. Wander around Shinjuku, you'll come across it guaranteed. Go at night.
--Meiji shrine (Yamanote to Harajuku/Yoyogi station IIRC?)--very nice, large shrine in the heart of Tokyo. Fill out one of those little wood boards you'll see with a wish and hang it up.
--Imperial palace (Yamanote to Tokyo station)--you can't go in, but may as well go see it to say you saw it. Truthfully though it can be skipped, as there is nothing else to see at all in this area despite being thrown off by the name of the station. Only go if you have time.
--Ginza--most expensive real estate in the world, and all high end shopping (and high end people). I believe you need to take the Ginza subway line to access it. There's an Apple store there as well (and in Shibuya).
Roppongi--has a reputation for being the sleazy part of Tokyo, due to the main strip full of illegal Nigerians and meat market clubs. Word is if you just want to sleep with Japanese girls, going to clubs here is like shooting fish in a barrel since easy 'gaijin hunter' girls tend to go here. My only advice if you go there is to wrap it up and ignore the Nigerians. However if you get off the main strip, you'll find numerous very, very classy restaurants and bars and more than a few ferraris rolling around. It's a shame it gets such a bad rap, off the strip I'd consider living there in an instant. Also go to Roppongi hills shopping. You have to take the subway to Roppongi station, but I don't remember what line.
Shinbashi--(Shinbashi station, not sure if it's Yamanote or not)--Oldest part of Tokyo, very beautiful and oddly enough it neighbors Ginza. Get off at Shinbashi station and walk along the elevated tracks towards Ginza and you will hit an area called "yakitori alley", an amazing place of maybe 10-15 open-air yakitori (delicious skewered chicken) restaurants wedged under the tracks with milk crate seating and red lanterns where the smoke and smell wafts up to the tracks. Get a big old beer with your yakitori, it's amazing. Must eat here. Keep walking, as long as you stay right by the tracks and are walking towards Ginza, you'll hit it in time. Maybe a 15 minute walk.
Harajuku--(Yamanote to Harajuku station)--Go here to see all the crazy fashion and goths of Japan.
Asakusa--Another very old part of Tokyo. Go to Senso-ji, very very famous temple in Asakusa.
There's millions of things you can do in Tokyo, and can eat anywhere. PRO TIP: If a restaurant looks expensive,
it probably isn't. Japanese are masters of restaurant aesthetics and ambiance, and they ALL look gorgeous/expensive/date-like, but you'll find cheap food to be had in most all of them. Also as has been mentioned--holes in the wall FTW!!!! Can't go wrong eating anywhere really.
Most places in Tokyo are best experienced at night, IMO.
Kyoto:
Getting around:
Kyoto is the ancient capital, it was the capital from 1194 until 1868 when the Meiji restoration moved the capital to Tokyo. There are over 2,000 temples and shrines in Kyoto city alone. Unbelievable. Truly Japanese culture at it's absolute unchallenged pinnacle. Due to this, there is not the network of trains and subways like there is in Tokyo, so this means you will be taking the bus everywhere but it's piss easy. Get on on the back of the bus, off at the front, rides for adults pretty much anywhere are a flat rate of 220 yen. There is a big bus terminal right outside the station that has signs in English listing everywhere every bus goes so no problems at all.
Dictricts to see:
Gion, Pontocho, Sanjo/Kawaramachi
Places to stay:
I recommend again any Toyoko Inn, or the Hotel El Inn right behind the station.
Things to see:
It's again impossible to list them all. You can spend months in Kyoto and not even scratch the surface. Here are a couple of the best IMO.
--The geisha districts of Gion/Pontocho. These are still the most elite geisha districts in all of Japan, and still have practicing geisha. Do not do a disservice/slap in the face to Japanese culture by even thinking for one second they are prostitutes or sell anything sexual. They are curators of Japanese tradition, extremely expensive to be entertained by ($1k an hour for 1-2 in some places), and it takes them about two hours to get dressed each day with the aid of a tradition-guarded trained dresser. So no, they don't flip their kimono up for 10 bucks. They are the guardians of the finest of Japanese traditional culture. If you are lucky--very lucky--you may be able to spot one. I had extreme luck when I was there, and saw and photographed a few. Make sure in Gion you go to the Gion Shirakawa part, it's absolutely beautiful. It is a very closed world, and the architecture of everything will reflect that.
--Ichiriki-tei: the most prominent and exclusive teahouse (where geisha entertain) in all of Japan. identifiable as it's right on the corner of Shijo-dori and the main road of Gion, and it's huge and has red walls. This was one of the places where the events of the 47 Ronin were planned 400 years ago.
--Gion/Yasaka shrine. Very close to Gion, at the end of the street (Shijo-dori IIRC)? Beautiful place, when I was there two geisha fluttered in in full regale to pray at the shrine as there was also a traditional wedding ceremony going on. Talk about cultural overload. Pics in my Flickr at the bottom.
--Pontocho--across the river from Gion, small and narrow geisha district with platform restaurants overlooking the river. Don't think you can just strut into these places--these places ARE expensive (mostly kaiseki ryouri cuisine) and are NOT open to the public--like the geisha world, this is a subculture of restaurants that cater to geisha and geisha clientele, which means longstanding personal introductions (think 20+ years) to access. There are a select few places that are open to the public, but only a couple and good luck reading the menus--they're all archaic old Japanese. Go with a Japanese person if you can.
--Kiyomizudera--Awesome temple, awesome view overlooking Kyoto.
--Kinkakuji--the "Golden Pavilion" covered entirely in Kanazawa gold leaf. Go as the sun begins to set, it's amazing. It's a long way from Kyoto station though, just FYI. But one of the most popular temples and when you go you'll see why.
--Philosopher's path--best done in spring with cherry blossoms, but this is a quiet canal that you can walk in twenty minutes to link (IIRC) Nanzen-ji and Ginkakuji (the "Silver Pavilion").
--Fushimi-inari--Awesome shrine up a mountain with lots of graveyards off the beaten path along the way. Over 10,000 orange torii. Spend a half day climbing this.
--Arashiyama--bamboo forest, was used in the Memoirs of a Geisha movie. Beautiful, almost magical place.
--Sanjo-Kawaramachi--T-intersection in downtown Kyoto with a bit of nightlife. Take the subway.
--Kyoto station--a marvel of engineering, built in 1997. Spend a little time just cooing over how sweet it is.
Seriously there are a billion places to go in Kyoto, it's impossible to list them. Do not skip the geisha districts.
Osaka:
Getting around:
Trains and subways. Osaka station is called Osaka station when it's the trains above, but on the subway lines it's called Umeda station, just FYI.
Places to stay:
Anywhere central, really.
Districts to see:
Umeda, Namba, Shinsaibashi, Amerika-mura
Things to see:
--Umeda sky building
--Osaka castle (though it's a modern museum inside with elevators and AC--talk about a WTF?? moment when I entered that, not knowing).
--Osaka aquarium--Cool aquarium right by the ocean. About $20 to get in.
--Shinsaibashi--best night time entertainment district and an Apple store. Also right outside Shinsaibashi subway station exit 7 (take the Midosuji line from Umeda) is Shinsaibashi Opa shopping mall. Want to see more smoking hot women? This is the place.
--Umeda--in the north, and more of a business district than a night time district.
--Namba--another good place to go for nightlife and eating.
Osaka is more of a nightlife place than a touristy place.
Nice thing about Osaka is it's location--25 minutes west on a limited express (less on a shinkansen) is Sannomiya station in central Kobe, and another 36 west from there is Himeji, with Japan's most beautiful castle. It's also a hop away from Kyoto on the same line.
Other places to see:
Kobe:
the classiest and most internationalized of all cities in Japan. Also the fashion capital of Japan. Truly, truly beautiful city. Foreigners in Kobe rank as having the highest satisfaction with quality of life compared to any other Japanese city. Go here and go to Port Island at night and look back at Kobe port. I would love to live here. Go to China town here as well. Good shopping and any kind of international food you could want, given the internationalized, forward thinking of Kobe and its people.
Himeji:
Just go that extra half hour on the train (or less on the shinkansen as that stops at Himeji as well, easy-peasy) to see Himeji castle straight down the street from the north exit of the station. Walk out of the station, boom there it is at the end of the street. The main tower is closed til January for a ten year renovation, but other parts of the castle are open, and the north side of the castle is the most beautiful so spend a little time walking around the north side by the moat (enter the castle grounds from the main front gate and stay right and you will get around to the back where it's quiet and there aren't any tourists.)
From Osaka you can hit Himeji in the morning, then head back and stop in Kobe for lunch and sightseeing, then be back in Osaka by night time no problem.
My hands are tired now, but there's a start for you. Below is my flickr to my first trip to Japan in 2007.
http://www.flickr.com/photos/aarontdenk/sets/72157605888956776/