As a resident of Vegas, I would say to get the car. What people don't seem to realize is that there are other things to do in Vegas outside of Las Vegas Blvd:
Hoover Dam.
Redrock Canyon.
Lake Las Vegas.
Route 66.
Planespotting at McCarran.
Planespotting at North Las Vegas.
Skiing.
Death Valley.
All are within an hour's drive of Vegas. If you're into scenic drives, I'd suggest Redrock Canyon, Death Valley, and Route 66. Redrock Canyon is only 20 minutes from any part of Las Vegas Blvd, as is the Dam and Lake Las Vegas. The rest are within an hour's drive. If you have the time, I'd say to make the drive down US 95 to Laughlin. 15 miles south of there, you'll pick up Route 66 going through to
Oatman, AZ. You'll find a nice little ghost town that has become rather popular, thanks to Laughlin and the Disney/Pixar movie
Cars, which talks about Route 66. The old route goes through the town. If you take it, you'll see some classic gas stations, cars on the side, and a really nice scenic route back to Kingman (also on Rte. 66). Taking US 93 North from there gets you back to Hoover Dam and Vegas.
It's snow/ski season here, and the best place for that is Mt. Charleston, if you're into skiing/snowboarding. That's only 30 minutes drive. Besides, where else can you go from 2000ft and high desert, joshua trees, snakes, and scorpions, to 8000ft with pine/conifer trees, deer, elk, and bear within 20 minutes time? Speaking of, another thing to think about is the weather. Yes, it's warmer than just about everywhere else in the country, but it is still winter. Do you want to have the wind (which this time of the year mainly comes out of the north/northwest) coming at you as you're walking down the Strip?
As far as staying on Las Vegas Blvd, it's easy to get from one place to another, if you know the right casinos to go into. You know about the tram between Mandalay Bay, Luxor, and Excalibur. There is also the Monorail, but it has had its share of problems. So what you could do is get out at Excalibur, walk down to Monte Carlo, take the tram from there to Bellagio, get out there, and you're at the Forum Shoppes at Caesar's Palace. Come out of there, go into the Mirage, and you can take the tram from there to Treasure Island (screw this "T.I." crap; it's Treasure Island, and remains that!

) Walk out to the front of Treasure Island, and you're at the Venetian. There are also shuttle busses between the casinos owned by the same company (Harrahs owns the Rio, Park Place owns Caesar's, NYNY, Excalibur, Luxor, Mandalay Bay, Bally's and Paris, MGM/Mirage owns MGM Grand, Mirage, and Bellagio), so you could get free rides from them too.
Oh.. If you do get the car, whatever you do, do not fill up the tank near Las Vegas Blvd. or the airport. You'll notice they will have the highest prices. Go into the college part of town (Maryland Parkway & Flamingo), or somewhere into the city proper and away from the tourist trap to get gas. you'll find cheaper prices that way.
Just some things to think about.
BL.