Arun's 4156 N Kedzie
Considered one of the best Thai restaurant's in North America. Even the NY Times has given this place great reviews and they usually pooh pooh anything connected with the midwest. It's incredibly popular so you have to make reservations way in advance, but you may be able to sneak in once in a while.
Cafe Lutz 2458 W Montrose
Mostly known for it's bakery. People usually go there for carry out. If you're a fan of German Pastries, particularly involving chocolate, nugout and marzipan you'll love it here. The cafe is also real nice. Try the hazel nut milk shake. The open face sandwiches such as tilsiter cheese and Westphalian ham are great. The tables are small and cramped and there's still some old fashioned German guests that don't believe in deodorant, but that adds to the charm. When the weather is nice, there's an outdoor cafe.
Red Apple Restaurant 3123 N Milwaukee
I don't think it's still true, but Chicago was once the largest Polish city in the World. There's still a large Polish community in the city, mostly along Milwaukee Ave. Red Apple is a friendly, inexpensive buffet. So you'll get to try a lot of different Polish dishes. They also sell frozen perogies to take home.
No particular restaurant. But head up to Devon and Western. The neighborhood is a blast. Very colorful and full of Indian Restaurants, Grocery stores and bakeries.
Late Night Drunks
Golden Apple 2971 N Lincloln
Just regular American Diner Food. It's open 24 hours a day. And this is where all the drunk northsiders go after closing time. It was once featured on "This American Life"
Army and Lou's 422 East 75th St
Long time Chicago favorite. Reasonable prices for Southern Cooking in a great atmosphere. Some of the friendliest and most efficient service you'll get any where in the city.
Besides pizza and hot dogs (make sure you get the day-glo relish to be authentic) another local favorite is Italian Beef. Which of course has nothing to do with Italy. You can get them any where.
Just some places off the top of my head. When I get some more energy I'll post some local attractions.