OK, I'm not the pizza afficionado, but is Chicago the same as Sicilian style? Because Masa in Echo Park is supposed to have a great thick crust Chicago style pizza. Haven't tried it myself, but everyone tells me it's great. If you go, get the bread pudding because holy cow is it amazing. I'm luke warm on their panini, but I've only tried two different ones. Quiche is good. Husband loves the meatloaf.
It sounds like you're in Pasadena, not Downtown L.A. Have you looked into gettin tickets to a show and then dinner in the real downtown area? We get stuck at home because of the fireworks - dogs being scared and such - but we used to go the Dorothy Chandler and then find food in downtown L.A. pretty easily. Or you can always get a car, go to Geoffrey's on PCH, (great place to view the sunset on the beach, or Charter House if they're not open), go to House of Blues for the crowd and Yamashiro for cocktails. Finish up at a local bar - - - - OH! hey, how about the Pacific Dining Car? Hell, I can't remember the exact name, but maybe somebody else will. Overpriced, but an L.A. land mark.