Well, I’d say that some improv/ sketch comedy should be seen, since Chicago is the city where the genre was honed. (It’s not an exaggeration to say that SNL probably wouldn’t exist or have survived as long as it has without Second City as an incubator).
Second City is the marquee venue, but obviously is the most tourist-frequented. I haven’t seen the current mainstage show, but the show in the smaller etc. theater has been running since last summer, and was absolutely hilarious last summer. I’m not sure how they’ve modified it since last summer, since some of the jokes that were funny then might be a tad dated now, but I’d recommend that show.
Smaller venues to look at are ImprovOlympic and ComedySportz. The quality of shows at these venues is somewhat more uneven, but often they’re entertaining and much less expensive than Second City.
A Cubs day game is a must. Not a night game. A day game. My fiancee, a die-hard Yankees fan and baseball purist, believes that what the Cubs play is not really baseball. Since I’m not such a purist, I tend to see the Cubs as providing a useful service, namely, getting Loop office workers out of the office early on Friday afternoons. You can also see a Sox game, but U.S. Cellular Field lacks the charm of Wrigley (and by charm, I mean “non-functional bathrooms”).
The Chicago Architecture Foundation sponsors a number of walking and boat tours of the city, which are quite good.
I second the endorsements of the Art Institute, the Field Museum, the Adler Planetarium, the Shedd Aquarium, and the Museum of Science and Industry. I’m more tepid about the Museum of Contemporary Art, though. Maybe it was just from living close to it for five years. But they often have interesting displays out front in the summer, and they do have a Solstice party in June which can be fun.
Neighborhood parties and festivals are also enjoyable. Here’s a list from theMayor’s Office of Special Events.
I’m not a huge fan of Taste of Chicago, but that’s because I live here and have the Taste of Chicago available to me pretty much all the time. If you decide to go, go during the daytime, not the evenings, and stay well clear of the Fourth of July, unless you really enjoy getting crushed by crowds.
I don’t know what your experience of large cities is, but the Magnificient Mile shopping area is a boulevard of big stores that really only draws comparisons with Manhattan. Again, having lived close to it for five years, its charms have worn off for me, but for someone who’s never been to New York, it might be an interesting experience. Just padlock your credit cards.
Outdoor music at Ravinia or Grant Park is a fun diversion.
Tons of stuff, really. Summer in Chicago is the time that almost makes up for the miserable winters.