Depending on what you're actually going for... the touristy things (like the aquairums and museums) are great. Another non-pseudo-educational possibility is simply to wander down Michigan Ave. That's the main drag for downtown retail, where shops and the fancy hotels are, etc., etc. That's the "downtown" part of "downtown" you want to be in. If you're staying overnight someplace, I won't even begin to attempt to tell you about any of the zillion restaurants... but there are no shortage of them within a few blocks off of Michigan.
Anyway, don't know how long you're planning to be there, but a walk down Michigan Ave, crossing the river (which will be cold & windy), and in that area is a very basic thing to do if you've never been downtown before.
Edit: Yeah... that's what its called, duh. "The Magnificent Mile." Your GF will dig that.