If you're coming into the city and want to do touristy stuff, stick with the mag mile or downtown area.
Hotels down there will cost you around $200-300/night. The Hilton is on the south side of Michigan Ave, and will give you walking distance access to the museum campus, the lake front, and Millenium Park. (Not to mention shopping about a mile up the street.)
You can also stay in the heart of the shopping on Mich Ave a little further north. The Allerton is a lovely hotel and is 1 block away from Water Tower and The Hancock.
There are also your W hotels (1 in te loop on Adams and 1 on LakeShore), the Trump, the Sheraton, etc...
All are well located for the tourist sites.
If you're going to a Cubs or Sox game, there are no hotels close to the parks, and frankly, you don't want to stay near Sox park. Cubs are in Wrigleyville, which is heavily residential (my neighborhood!). Terrific for a visit, game and walking around. Lots of nightlight for 20 somethings. But you won't find much else to do around there for the traditional tourist activities.
Check out the street fests, as well, depending on when you're coming. Ribfest is this weekend - which is AWESOME.
Here's a link to the kid friendly festival calendar. I highly recommend this if you're coming to town. The tourist stuff is fun, but the festivals in the neighborhoods will give you a true 'feel' and taste for the city at it's finest.
http://timeoutchicagokids.com/things-to-do/140921/festiva...