First and foremost: if you are at all a baseball fan, you are going to want to spend an afternoon at Wrigley Field. Friday afternoons are usually the liveliest, as half the city seems to play hooky. Night games are still rare at the Friendly Confines, and are also fun, but for the true experience, you need to make sure you go to a day game.
The Field Museum is currently quite popular, thanks to Sue (a very complete tyrannosaur skeleton). Also, the aquarium/oceanarium (adjacent to Field) is a lot of fun.
In the evenings, there are numerous good neighborhoods in which to party. Lincoln Park and Wrigleyville are always common, but I also enjoy the more out of the way places, such as the smaller Italian neighborhood near UIC.
Quick Tips:
For some museums, you will encounter a line to enter. If this is the case, and you are in a group of 2 to 4 people, consider buying a membership to the museum. Usually there is no line to do this. Weighing the costs, you might find that it's not much more to join the museum, especially if your group wants to see special exhibits. For example: at the Field Museum, admission plus all special exhibits can sometimes run or so per person. Out-of-state Museum membership costs for 1 year, and includes two free passes to everything, with discounts on additional passes. If the wait to buy tickets significant at all, you might as well go to the "Member's Only" area and sign up. We did this five years ago at the Field Museum to avoid a line, and we're still hooked...
Other museums have "suggested" admission fees (i.e., donations). I usually give the suggested fee - or a dollar or two more - but I suppose you could theoretically get in for less (i.e., the Art Institute).
Best Way To Get Around:
If you are spending time in Chicago proper, you will be able to use trains to get to most places. A rental car is only necessary if you are going to be based in the suburbs. Traffic to/from the airport can be absolutely brutal at times, and driving in the city requires a great deal of local knowledge.
The Blue Line from ORD takes you right downtown. Cabs are everywhere in Chicago, and even locals use them on a regular basis as a primary means of transportation. You should do so too if the trains aren't convenient - you needn't be afraid of Chicago cabbies; most of them are quite friendly, and the cab prices are standard and straightforward. Some cabs do NOT take plastic, so have cash on hand.