I live here. Here are the ABSOLUTE MUST SEE SPOTS:
Field Museum (has huge dinosaur bones, reconstructed)
Millennium Park
Navy Pier
Art museum if you like art (and definitely see "American Gothic" if you can -- it's the painting of the farmer and the wife with the pitchfork--it's very cool to see in person. Also, they have lot of Van Gogh, Picasso, Renoir, and other famous artists in there.)
For Chicago pizza (the sauce goes on top of the cheese), check out Gino's east - the grafitti on the walls alone is worth it and if you bring a white marker or toothpaste, you can make your own mark there. It's their "gimmick." Though Giordano's pizza, Pizzeria Uno, and Edwardo's are slightly better pizza, you can't write on their walls, and Gino's East is famous and fun.
If you like funky little shops, walk along Broadway from about 2800 North to 3400 North -- lots of small shops with unique things in them.
If you like exclusive boutiques, check out the shops on Oak Street. Try not to faint when you see the prices!
Take a boat ride at Navy Pier or on the Chicago river--both are excellent. If you take the Chicago river tour, you will see a lot of the architecture in the city, if that interests you.
Don't pay money to go to the Sears Tower or the John Hancock building--it's a waste. Just go to the John Hancock building and have a drink at the bar on the 96th floor. The view is spectacular (almost the same as the viewing deck view) and there's no admission price to get into the bar. The Sears Tower is a ripoff--steer clear.
Lincoln Park Zoo is in the middle of Lincoln Park and is free. There are also paddle boats you can rent. It's beautiful.
If you like shopping, 900 N. Michigan and Water Tower place are upscale malls on Michigan Avenue ("The Magnificent Mile") so be sure to check that out too.
Oh--catch a Cubs game at famous Wrigley Field and have a drink at the Cubby Bear afterwards. Sit in the bleachers if you like to party and get sun, or sit in seats if you're more subdued and actually want to pay attention to the game.
Have a great time in Chicago -- it's a really fun city. Good luck!