Places to go in Chicago

Hello there Vergers!

Next month, I will spend a few days (5 to be precise) in Chicago on vacation, and being my first time there, I would like to hear if you have any suggestions on fun places to go.

I plan on doing all the touristy stuff, but feel free to suggest tourist things anyway, if you feel it is something that can't be missed.

But if you have any geeky gems for visiting, awesome!

Also, recommendations on good places to eat and drink will be highly appreciated (I eat pretty much everything, all kinds of animals).

Thanks a lot!