Depends on what you're looking for, brewery or brewpub. As far as breweries there are lots of good ones around. Half Acre is my favorite place, they do tours on Saturdays. The tour will be full already but if you just show up and walk in they don't care. It's one of the best tours I've been on and they have great beer.
Metropolitan also has tours on select Saturdays. It's a small brewery run by a young couple and they have good beer but the tour isn't as good.
Goose Island is the classic Chicago brewery. Their Sunday tour is pretty good and they have a great restaurant.
Three Floyds is south of town. I didn't like their tour or their beer. They over hop everything which just isn't my thing. They do have a nice restaurant though.
Two Brothers is in the west suburbs, it's one of my favorite places. They have great beer and a great restaurant.
As far as brewpubs I'll just list a few of my favorites:
-Piece-New haven style pizza and awesome beer (my go to pizza place, skip the deep dish)
-The Map Room
-Haymarket pub (Just opened, haven't been here but I've heard good things)
Let me know if you have any questions