Well, checking out the shopping on Michigan Ave is worth a look. The Chicago museums are all great -- in particular the Art Museum (also on Michigan Ave - south end, I believe), Museum of Science and Industry and Museum of Natural History are pretty cool. You can go up in the Sears Tower and/or John Hancock buildings for views of the city. Baseball season should be going, so if there's a home Cubs game that would be well worth checking out -- bleacher seats should be pretty cheap and probably the most fun seats in the house. In fact, Wrigleyville - the area around Wrigley field - is full of fun bars & restaurants (at least last time I was there, but I can't imagine it's changed all that much). Not sure I'd recommend seeing a White Sox game only because the ball park is in a pretty rough neighborhood.
There are just too many great restaurants to name - as you find in any big city. If you like steaks and can find Baloo's recommendation, I'm sure you won't be disappointed. If you're at all into pizza, then you need to try authentic Chicago pizza (deep dish) and Pizzera Uno is probably the most well-known place for that.
I'll keep thinking
Edit: I remember having some fab breakfasts at this place:
Ann Sather I don't remember which location - they may have only had one at the time anyway. But it looks like most of them are downtown-ish anyway.
Edit Again: How could I have forgotten the Shedd Aquarium??! It's in the same area as the Science & Industry and Natural History Museums. Also seeing a lot for Navy Pier - I think it's been built up quite a lot in the past 10 years or so - last time I was there we did have lunch out there and went to a children's museum there - probably not your thing

However, I did see a lot of boat tours/cruises available there, so there might be something worth checking out and as it will be well into May, the weather should be quite nice for a boat cruise.