I’d completely disagree with Sarahfeena, but that may just be the way I like to travel - get into the neighborhoods, go as far away from Michigan Avenue as you can. The one don’t-miss spot in River North (tourist area) would be Pizzeria Uno or Pizzeria Due (I prefer Due), that is the real deal Chicago deep dish. Gino’s is also the real deal.
I’d say, while we are famous for deep dish pizza, an even more authentic Chicago meal would be an Italian Beef. The best is Al’s, on Taylor Street in Little Italy. There’s also an outpost in River North, probably just as good but experiencing Taylor Street would be more fun, plus you can follow it up with Mario’s Italian Ice.
If the Cubs are in town, that would be a great way to spend a day. Either in the ballpark or on a rooftop.
If you like art, the Art Institute has a collection of Impressionist paintings that will take your breath away, and the MCA has a swiftly-rotating collection of great contemporary works, lots of installations and avant-garde video stuff, plus it’s cheap and usually not crowded at all.
All summer long, each weekend has a couple neighborhood street festivals, featuring a variety of local food and music. If you want a taste of what Chicagoans do for fun, a neighborhood street festival would be a good bet. You can probably find out where they’re happening at metromix.
If you like seeing indie bands in small venues, check out the Empty Bottle, Double Door, or Subterranean, all in Wicker Park. Metro, Bottom Lounge, and Martyr’s generally have pretty good booking too.
Millennium Park is a tourist trap, but the Park Grill has good food and this summer there is a series of free shows on Mondays at noon and 6:30. Whoever booked these bands (mostly rock and experimental) did a great service to our fair city, you should at least see who’s playing if you’re here on a Monday.
If you want to dance to beats, you have a ton of options. I’d recommend Sonotheque (cheap and pretension and dress code-free) or RedNoFive (slightly more pretense and druggier), or if you want the big Chicago Megaclub Experience, Crobar or maybe Soundbar.
One more thing - Chicago is not known as a mecca of Indian food, but if you like Indian food, go up to Devon Avenue. Tiffin is my favorite, it’s American style white tablecloth service, full bar, and amazing food. Others like Hema’s, which is grittier, arguably more authentic, cheaper, and byob.
Have fun.