For killer ribs, take the Blue Line to the Jefferson Park stop; exit the station and look for the Gale Street Inn across the street.
Or take it down to the Chicago stop, and look for the Silver Palm restaurant (face the city and look for the converted Pullman railroad car). Order the Three Little Piggy sandwich. It's incredible.
If (when) it warms up, stop at the Belmont stop, head towards the lake. When you hit California, turn left and go to Hot Doug's. Best damn gourmet hotdogs in town. Alligator, bison, ostrich, venison... He's got something unique every day, and it's all awesome. Duck fat fries on Fridays and Saturdays. Expect to wait, cash only and he's only open from like 10am to 4pm.
(You might be tempted to stop at Kuma's Korner for a burger (it's off of Belmont, close to Hot Doug's.) Skip it. Lousy service, the staff is rude and the ingredients don't justify the price. Instead, make your way to Lincoln Square and go to The Bad Apple. Try "Elvis's Last Meal". It's peanut butter. And bacon. On a burger. Out of this world.
You'll find a dozen phenominal joints within a 5 minute walk of the Logan Square stop; El Cid (Mexican) and The Rocking Horse (everything) are both great.
Chicago is a Mecca for incredible food. I can't wait to get back.