You can get the city pass which gives you 5 attractions (Shedd Aquarium, Skydeck Chicago on top the Sears Tower, Field Museum, Museum of Science and Industry or John Hancock Observatory, Adler Planetarium or Chicago Art Institute.
Personnally, we chose the Shedd Aquarium, the skydeck, the museum of science and industry and the planetarium. If you're into Art, the Art Institute has a good reputation I think.
We didnt choose the John Hancock because we thought it would ressemble to the Sears Tower, and you can get up the observatory by going to the bar up there (with purchase of a drink, which costs around 15$).
As Ti Pit said, Millenium Park is pretty cool for a walk. Close to it, go check out the Cloud Gate (The big bean) and the scene is great for pics. Also, close by, there are the water fountains with the faces.
I think there is also the Chicago Zoo close too, it's free!
Magnificent Mile is like the Fifth Avenue of NYC, but in less fancy.
The Chicago Harbour (pier) is nice as well, this is where they shot some scenes of Transformers.
To fully understand the richness of the architecture, get a guided boat tour on the Chicago river. Since the river is in the middle of the city, you get to see a lot of the buildings. The guides are very friendly and explained well the history of the city.
Also, close to the Chicago river is Wacker Drive. At night, it's freakin' amazing with all the lights of the buildings. You get to see the variety of architectural masterpieces. And it's the street where a lot of the Batmobiles scenes were shot.
Last but not least, if you can see a baseball game at the Wrigley Field, it's always nice! Dunno if the season started though.
As for the Deep-Dish Pizza, we ate ours in Uno Pizzeria. It was worth the 30 min wait.
Have fun! I really enjoyed the city!
PS: Although the % of crime is high in Chicago, I found the people really nice vs. NYC.