I concur with Tom... the Art Institute of Chicago, and the Museum of Contemporary Art... two great art museums. If you're looking for other worthwhile museums, the Field Museum, and/or the Adler Planetarium are wonderful, as well as the Shedd Aquarium and it's live northwest dolphin show, and the Museum of Science and Industry... all world class venues.
As far as non-chain restaurants... of course, Chicago is well know as a town with many steak houses, surely Gibson's is one of then, Mortons, The Palm, Gene & Georgetti's & Ruth's Chris, excellent if you're looking for a good steak (in some cases large enough to be considered a roast!), for more unique Chicago dining, you might try OneSixtyBlue (Michael Jordan's restaurant) in the river north area, Pasteur (vietnamese/french) a bit further north, or in Pilsen a wonderful place called Xni-Pec (Shnee-Peck), Irazu (the cities' only bona fide Costa Rican Restaurant) which is a hole-in-the-wall on Milwaukee, and lastly for a fru-fru contemporary Japanese restaurant, Japonaise on Chicago is very exciting.
I'm sure more people will add their favorites... there are just too many places to choose from in Chicago... it's kinda like asking where to shop!! don't get me started.