Try Calo's, way up in Andersonville, I think on Clark - I used to order Linguine Carbonara (which is to die for!), but now and then I'd get the ribs - very sweet and tender. And reasonable.

Also, don't know if it's still there, but there was that rib shack place on Irving Park Road at Ashland, around the corner from the Ten Cat. Supposedly very, very authentic, but I always found their ribs too tough.