It's pricey staying downtown, no matter what you do. But for a much lower price you can get a private room in Hostelling International's downtown location that comes with a free breakfast, too! The facility is very conveniently located, clean, friendly, and well-secured at night.
Next door, stuff your face with beautiful pressed sandwiches, homemade soups, and Cuban-style coffee for prices you usually only find in the outer 'burbs at Cafecito. I went twice: once for the traditional Cubano (roast pork, ham, Swiss cheese, mustard, and pickles), and again for the Chimichurri (steak, tomato, and super-garlicky chimichurri sauce). The grilled cheese with guava was awfully tempting, though...
Want to pig out on delicious eggs? Go to Yolk (which I reviewed a couple of years ago.)
Booze is expensive in fancy hotels. Gino's East South Loop has deep dish pizza, if you eat that crap, but they also have a great list of local beers, something I never thought I'd see catch on when I was growing up in Chicagoland in the 80s. So, go here, because you know someone you're with is going to want to eat that ridiculous pizza-casserole. Then you can walk a few blocks towards the lake and hear some great bands at Buddy Guy's Legends. It's a little touristy, but the music is legit.
If you are in no hurry (really, the service is terrible), stop by the old crusty Artist's Cafe across the street from the Art Institute museum and school. The cappuccino is the best, and the decor is old-school Chicago:
Touristy stuff to do along Lake Michigan, in no particular order: visit Millenium Park and gawk at the weird interactive art, stare at the giant metal bean, and run through the fountains; go to the Art Institute, for goodness' sake!; rent city bikes and ride along Lake Michigan; visit the museum campus, which includes the Shedd Acquarium, Adler Planitarium, and The Field Museum; go to a Chicago Symphony Orchestra concert; visit the amazingly beautiful public library at State Street and Congress; shop for stuff on State Street; people watch in Grant Park (and on summer mornings, hear the Grant Park Symphony rehearse for free); visit the Museum of Contemporary Photography at Michigan and Harrison; take advantage of public transportation as often as you can, because it will take you anywhere you need to go!
This is all within walking distance, basically up and down Michigan Avenue and thereabouts, but you can see it all on a map here.