I'm sure others can add on here:
Oak St. just west of Michigan Ave. has a ton of fantastic shops. There' s Independence, Jil, old Y-3 (now just stocks high end Adidas), Gallery Aesthete, Barney's. Michigan has some cool stuff on it too, the Nike store is pretty neat, heard good things about Ralph Lauren store, also lots of fast fashion (Zara, H&M, Topman, All Saints). Also consider checking out Haberdash, Patagonia, and Suit Supply.
Chicago is known for deep dish, there are 4 places within a 2 block radius on Michigan that are great. Pizzaria Uno's/Due's (same place, just two separate locations), Gino's East, and Giordano's. If you're looking for some fine dining, head north on Rush and you can find a couple of nice restaurants (Tavern on Rush is great, albeit $$$).
Stuff to see:
Bean in Millenium Park is pretty standard tourist fare, with a distorted picture. In the area, you could see the Sears (not Willis) Tower, but IIRC it's like $20 to go to the top. There's a couple of cool museums in the area. Field Museum and Shedd Aquarium are both a bit south of the "downtown" area, but they're both fun. Art Institute and Museum of Contemporary Art are both pretty close to downtown Chicago; MCA is a lot more reasonable though ($12 for adults, $7 for students).
"Let's be vagabonds." - Yohji Yamamoto