Check the Lettuce Entertain You website for locations near the Sheraton. Their events team is always very helpful.
Other ideas include The Dearborn, Remington's, Tortoise Supper Club, River Roast, Barrio and Siena Tavern. I've done small group dinners at the first three and have researched the last three but haven't pulled the trigger on them.
I don't know the area around UIC as well.
Good luck!
-Mary