Nowadays most convenience stores have ATM machines, and as long as you're in the city there are banks around every corner, so you should be fine. But yes, do try to carry around some cash while you're there. ¥10,000 should be more than enough if you aren't planning to do much shopping - if you are, think accordingly, but most proper stores in Tokyo accept VISA or MasterCard so don't fret if you find yourself low on cash.
Naeba is one of the best ski slopes in the country. It's an hour and some ride from Tokyo station using the bullet train - it's three stops on the JR Shinkansen MAX, the fare is ¥6,500. Here is an English site on
Naeba.
In terms of Sumo, you're just going to miss the March tournament - it starts on the 9th. The January tournament was awesome, with the long-time champion Asashouryu back from his two-time ban, up against the new champion Hakuho - and the final battle between the two with Hakuho finally throwing Asa down... man that was an
exciting match! ... but I digress...
Baseball season starts in late March, so you're out of luck there again.
One question: Where will you be staying? This relates to my first tip...
Tips of my own:
Take the subway/local trains. They'll take you everywhere. And get a
Suica. These are basically prepaid subway cards, but with the über-cool convenience of wireless IC chips embedded in them.
So basically you don't even have to get these cards out of your wallet to use - as you go through the ticket wicket, you just "touch" your card on to the Suica pad, and the gate opens. No hassle with tickets, no hassle with taking stuff out from your wallet (as long as the card isn't hidden deep between other things in your wallet, you can just "touch" your wallet and it should be able to read it). Best of all - you don't have to worry about how much the train fare is going to be. Since the Tokyo train system's fares change after every 5 or 6 stations you pass and/or every line you change, standing in front of the ticket machines, figuring out how much you have to pay ends up wasting a lot of tourists' time. With the Suica, as long as you have enough money on the card, you can get off and on trains without need to worry. - Now, where can you buy a Suica? These can be purchased at a Suica vending machine at any station that has Suica - but this is why I ask where you're going to stay...
As for knowing where to go on the train lines... this is one English site where you can enter the name of the station you want to start from and where you want to end, and it will find the best route to take you there.
Tokyo Transfer Guide. It's kinda shoddy, and it's not what I usually use, but it's the only decent one in English that I found. It has most major stations, so see how it works out for you.
Walk. See the city. It's one of those places.
Don't be afraid to ask people for help. While Japanese people might seem rude at first, that is just their shyness, no ill will (for the most part). Ask around and you'll find someone willing to interpret your English and/or hand movements and help you out.
Stay away from Kabukicho - it is the shadiest part of the city. If you're in the mood for clubbing, wanting to meet other foreigners, then going to Roppongi isn't a bad idea. But seeing that you're only in Tokyo for a week, I'm sure you won't be feeling homesick so soon.
And as obeygiant mentioned: enjoy the food. The best from around the world can be found in Tokyo, so if there's a day you want to have something other than Japanese food, don't be afraid to look around. Roppongi has evolved into a great culinary town, with the
Roppongi Hills and
Tokyo Midtown complexes that have opened in recent years. Try Ginza if you want to go for even more upper-class stuff.
Oh, and if you're ever in the mood for Indian food (Indian food in Japan?), go to
Samrat. The best in Tokyo. My family business.
Roppongi Hills' Mori Art Museum and Tokyo City View are also great pastimes if you're in the mood.
Any more questions, you are more than welcome to ask.
irmongoose
