You might get lucky, but the weather is generally still pretty crappy in late March: 30s, 40s, and 50s; drizzle, maybe some snow, and certainly lots of mud. At least you won’t have to be tempted to attend opening day at Wrigley or Sox Park.
You could do a couple of museums superficially, or one really well: The Field, The Shedd Aquarium, the Platerium (all three are within walking distance of each other), the Museum of Science and Industry, or the Art Institute. Pick one based on your tastes.
You could visit some local restaurants and bars, of course. The River North area is littered with world-class dining and drinking establishments. You could shop on North Michigan Avenue, visit the observation deck at the Hancock or the Willis (nee Sears) Tower, or take the architecture boat tour on the River.
There are plenty of neighborhood tours, too, if you have a particular interest in a particular ethnic or otherwise specific neighborhood. You can also pick a guide book and do a self-guided walking tour.
Good cheesy fun: the Untouchables Tour, a black, bullet-ridden school bus whisks you around town to see various gangster landmarks, while costumed guides regale you with amazing tales of our gangland heritage.
There are several “pizza tours” also, which let you sample a variety of the city’s best offerings of various types of pizza. Also, the Chicago Food Planet tour is interesting.
Here is a bog entry with “Ten Perfect Chicago Experiences.” I’ve done just about all of them, and if they sound like your cup of tea, you can bet they will be fun.
Have a great trip! Let us know what you ended up doing, and how you liked it…