Pizza:
Depends on what side of town you're on, but here's some of my favorites:

Giordano's
Home Run Inn
Pequod's
Italian Fiesta
Lou Malnati's get a lot of love, but I'm not a big fan. It's ok, though.

Clubs/Bars:

Promontory (good place to see a show, but the staff sucks.)
Thalia Hall/Punch House
Harbee's (mostly DJ's)
The Whistler (cheap drinks!)
Subterranean (depends on the night. It can go from 'awesome' to 'suck' in a hurry)
Metro/SmartBar
Crocodile (kinda sucks, but it's always packed. Your level of tolerance depends on your age)
Revolution Brewery (craft beers and all that kinda stuff)
Emporium (arcade games and booze. Two locations)

Records/CD's:

Reckless Records (the Wicker Pk one is awesome)
Dusty Groove. Best record store in Chicago, period.
606 Records
K-Starke Records
Hyde Park records
Gramaphone Records