I went to high school in st. louis, and I just returned last year to work at WashU. I live in the Central West End. If you end up going to SLU, the South Grand area is a cool place to live. The city has a lot of charm and living in the City is a lot more convenient than the suburbs (traffic will be a bitch soon since they're shutting down highway 40 soon, which is the main vein of traffic). Some people (*ahem* one of the previous posters) may say that the city's unsafe, but that's pretty exaggerated. Particularly around SLU and WashU, the schools are both very concerned with campus safety, so there's a lot of police patrol. As with any urban area, you just have to be street-smart. In medical school you'll need all the time you can get, so don't waste it commuting from the 'burbs.
You'll also notice that St. Louis revolves around FOOD. Whenever I have friends visiting, my list of things always ends up being eating at such and such place. For an uber-cheap meal around the south Grand area, try Pho Grand, it's a vietnamese place. Around the central west end, I'd recommend Dressel's or Llywelyn's for some welsh chips and a beer. The U-City Loop is a fun place to walk, and you can check out Blueberry Hill. As far as touristy things to do, you should go to the Arch (as a st. louis resident I don't think it's cool at all, but I've heard from quite a few med school applicants that they've enjoyed going up close to it), drive through forest park, the zoo is free, and if you have some time to play, go to the City Museum. It's like a giant jungle gym (if you go at a good time to avoid the masses of kiddies).
have a great visit!