Within walking distance of the Hilton is Miller's Pub. It's decidedly midwest American, not touristy (even though it's next door to the PalmerHouse) it's a popular lunch and dinner place ith people who work in the loopIt's large menu ranges from sandwiches to complete dinners and has a good bar.
http://www.millerspub.com

I've only eaten at the Florian which i like very much, but I've heard good things about the Pederson Room.

For your pre-opera dinner you might consider eating at the opera house. See:

http://www.lyricopera.org/yourvisit/d...

In Hyde Park: http://www.medici57.com

Farther south: /http://www.bjsmarket.com/

Oasis Cafe, a Middle Eastern restaurant located at the back of the Jewlelers Mall )itself a rather fascinating place), 21 N Wabash

http://chicago.metromix.com/restauran...

If you want to see plays check out the League of Chicago Theaters:
http://chicagoplays.com Click Shows and Tickets.

7start_28

Just a little way down the road from Corolla is the Sanderling Inn. Its dining room serves an extremely good brunch (lunches and dinners).

http://www.thesanderling.com/

Well off the beaten track, in the south side Chatham neighborhood is the Black Hebrew restaurant, Soul Vegetarian East. The the web site from PBS TV show, Check Please, included this video:

http://www.youtube.com/watch?v=ZYRZSfTCCtY

The Chicago Tribune's Metromix had this review:

http://chicago.metromix.com/restauran...

A couple of places I don't think anyone has mentioned are a fairly new Asian Fusion restaurant, Chant, and a well established middle eastern one, Cedars of Lebanon. Both are on 53rd St., a short drive but a pretty long walk from the museum. Here are their web sites:
http://www.chantchicago.com/
http://eatcedars.com/default.aspx

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Asian Fusion
4601 Lincoln Hwy, Matteson, IL 60443