Unless you are going to see a matinee, your post-theater options right in the neighborhood are limited. First, not many places are open much past 10 p.m. Second, the two parking garages nearby both typically require that you move your car within half an hour after the show ends.
My suggestions would be to either eat beforehand (in which case there are lots of options within walking distance, including several whose valet will happily park your car before dinner and let you retrieve it after show) or head for Greektown or Chinatown afterwards.
If the show is a matinee, or you want to eat early, my top choice would be Vinci, which offers regional Italian fare -- very good pastas, cacciucco and the not-to-be-missed polenta con funghi.
Vinci
312/266-1199
www.davinci-group.com
1732 N. Halsted St.
Chicago, IL 60614