Here would be my advice for visiting Chicago: Don't just do the tourist stuff. Especially stay away from the Rush/Division area, unless meat market bars are your thing.
Of the museums, they are all outstanding. My favorite is the Museum of Science and Industry in Hyde Park. After that, it would be a tie among the Field Museum, the Shedd Aquarium, and the Art Institute.
If you are going to do one of the tall buildings, by all means do the Hancock -- way better views than Sears. Instead of paying $18 just to walk around, go get a cocktail and sit at the bar at the Signature Room.
Navy Pier is a tacky tourist trap. Not worth a visit unless you are taking a boat tour.
If you have time during the day Friday, a great way to see the city is to take a Chicago Neighborhoods bike tour -- not the one that does the mag mile -- do the one that goes through Lincoln Park.
Restaurants. First choice for a first time visitor would be either (1) Gibsons Steak House or (2) Shaws Crab House. Both are Chicago institutions. Beyond that, Unos for deep dish pizza, Felony Franks for dogs, Spiaggia for italian, Cafe Ba Ba Reeba for tapas, and either Frontera Grill or Topolobompo for Mexican (both owned by Rick Bayless). If you are downtown for lunch on Friday, go to Xoco, Rick Bayless' casual Mexican sandwich restaurant -- literally the best sandwiches I have ever had in my life.
Bars -- Do a blues bar or a jazz club. In my opinion the best blues bars are Buddy Guys Legends or Kingston Mines. Jazz clubs -- its been 10 years since I have been to one, so I can't recommend anything.
Nightlife generally -- spend time in the Lincoln Park neighborhood. That is by far the best place to spend time at night.
My main advice is see the city a little beyond the big tourist sites.