For anyone used to New York and San Francisco, Chicago is always surprisingly inexpensive, so be sure to seek out and take advantage of the cheap meals and one dollar beers. The major highlight of Chicago is the downtown architecture, easily the most impressive of any U.S. city outside of New York. Many visitors try to experience Chicago's architecture by way of an elevator ride to the top of the Sears Tower, but you're probably better off simply strolling downtown while looking up. If you must view the skyline from above, though, I would recommend a free trip the John Hancock Building bar where you can enjoy the view and a beer for less than the price of summiting the Sears Tower.
Depending on the weather, another highlight of Chicago is the Lincoln Park Zoo. Really, one of the best things you can say about the city is that it can support a free zoo open 365 days a year. Unfortunately, I wasn't able to visit during my most recent trip, but the Farm in the Zoo exhibit (and in particular the goats) shouldn't be missed.
Quick Tips:
Having lived in Chicago for four years, I would strongly suggest planning your visit for the summer. Chicago is at its best during the warm months when locals cut back on their work hours and spend more time relaxing in parks and along the lake. All summer long there are also plenty of neighborhood- and city-wide festivals, the biggest of which is Taste of Chicago. The crowds to this event can be a bit overwhelming, though.
Instead, perhaps think about simply catching either a Cubs or White Sox baseball game (one or both of the teams are usually in town) or just sit out on one of the city's many patio bars and enjoy a cheap beer.
Finally, if you want to get a sense of Chicago culture beforehand, I would suggest reading anything by Mike Royko (especially Boss), the poetically brutal Chicago: City on the Make by Nelson Algren, and the comic work of Chris Ware which beautifully depicts Midwestern melancholy.
Best Way To Get Around:
Situated on the shore of Lake Michigan, Chicago is a very long, narrow city, running some 20 miles from north to south. This means that if you need to go across town from say, Wrigley Field to the University of Chicago, be prepared for a long drive and a fairly expensive taxi ride. The city does have the EL(evated) Train (.75 per ride), but very often you'll have to transfer to a bus (an additional 25 cents) to finish your trip. As with most major cities, driving and parking are a hassle, so you're best off leaving the car at home.
Also be forewarned that a trip to O'Hare Airport by public transportation is something of an ordeal, so give yourself at least an hour and a half to complete the trip from downtown.