Agree with KG. Yes, as long as you're here, just go for it and go to Alinea. Some say it's the best restaurant in the country! (Gourmet mag? Can't recall.)
Everest - very nice, though I can't say I loved it. And KG - as a traditional classic French lover, isn't that more Alsatian than classic French?
This month's issue of Chicago mag voted this as best new restaurant in Chicago. Haven't been there, but it's on my list (of restaurants that I never get a chance to go to, but really, really want to.)
http://www.goosefoot.net/