This is a loaded question because there are so many great places to eat in this city!
Here are a few of my favorites:
Gilt Bar (River North Neighborhood)
-Really great, simple yet elegant food done in an unpretentious atmosphere. Try the foie & pork liver on toast. Great cocktails as well!
North Pond (Lincoln Park)
-Five time James Beard award nominated Chef Bruce Sherman doing seasonal, farm-to-table food.
Twist (Lincoln Park/Lakeview)
-The best Tapas I have found in Chicago so far.
Old Town Social (Old Town)
-Amazing selection of house-made charcuterie and a huge beer list. Nuff said.
Chicagos Dog House (lincoln Park)
-Forget Hot Dougs, the place is overrated, never open, and there's sure to be a line when it is. Great selection of vienna beef hot dogs and specialty sausages. Try the smoked duck sausage with honey glazed pears.
Bari (Little Italy, I think?)
-Tiny little deli that does the BEST sub sandwiches on fresh bread from the bakery next door.
Coast (Bucktown/Logan Square)
-I am not a big fan of sushi, but this place is really great.
The Publican (West Loop)
-Meat, meat, meat, and more meat. Awesome house-made charcuterie, and a great selection of seafood as well.
Man, oh man. I realize this list can go on forever so I'm just going to cut it off here. All of these places are great and not at all touristy like some of the others I've seen on this thread.