Anywhere but Geno's East
Don't fall for the trap that Chi-town folk play on outsiders. They say it's really good pizza but it's NOT EVEN CLOSE to worth it. It's my belief that the restaurant only survives based on tourism at this point, because nobody would possibly go there twice.
Joe's on East Grand is my favorite Chicago restaurant. Lawry's off of Michigan Ave on East Ontario is a Chicago institution. Keefer's is my favorite steakhouse, though Gibson's is great, too - their dessert portions are generous, hehe. If you want to hit up Greektown, I like Greek Islands.
Best pizza in the city (yeah, I said it) here: http://www.pequodspizza.com/
Giant sandwiches to soak up liquor: http://www.luckysandwich.com/
Also, if you're downtown proper, this place opened up recently, has some nice brews: http://www.haymarketbrewing.com/