Just a few minutes away:
Prairie Grass Cafe: Casual place with chef Sarah Stegner, formerly of the four star Ritz Carlton. I'm not a big fan, but most people seem to really like this. Modern comfort food with a gourmet touch.
Francesco's Hole in the Wall: Very good Italian. The only problem is they don't take reservations, and it's very popular. Call from your car as you're leaving the BG, and they'll put you on the list.
About 15 minutes away in Highwood:
Miramar: a French bistro (with a minmal Cuban influence) run by Chef Viti, currently of Gabrielle's (more high end) and formerly of Carlos (very high end). Good, simple, frenchy faire.
La Casa Del Isaac: Just opened Mexican place. See the thread on this board where it is getting uniform raves.
Evanston is farther than the above, but probably within 20 minutes, and that opens up a whole other bunch of places. If you're going back to the City, your headed in the right direction.
Jonah