If you’re looking for real barbecue ribs (this means not braised or boiled, but cooked over wood and/or charcoal slowly, you know, the way God intended for ribs to be made), among barbecue afficiandos, there is pretty much a consensus that the best examples are Uncle John’s, Honey 1, Barbara Ann’s, and Lem’s. For ribs, my favorites are either Lem’s or Honey 1. For rib tips and links (what I normally get at a Chicago barbecue joint), my favorite is Uncle John’s. Except for Honey 1, none of these have dine-in options and they are located deep in the South Side. Honey 1 is a West Side barbecue joint that relocated to Wicker Park. The owner, Robert Adams, is from Arkansas and knows his way around an aquarium smoker (the predominant type of smoker used in old school Chicago barbecue in the African-American/Southern tradition, and also the type of smoker you’ll find at Cozy Corner in Memphis.)
My recommendation is always to ask for sauce on the side, so you could taste the meat itself, and then sauce to taste. The Chicago tradition is, generally, more sauce-heavy, though.
In my opinion, Carson’s and Robinson’s are not very good (or, I should say, not to my tastes.) And if you’re talking about Hecky’s that became Hickory’s (on Halsted), that place is utter crap. Hecky’s in Evanston is better, but still second- or third- tier for Chicago barbecue.
If you want a more sit-down, family friendly dining experience, there’ve been a couple new joints that opened up in the last few years. The best among them are Smoque and Honky Tonk barbecue.
Given the nature of barbecue and your timing, your experience can be hit-or-miss. I’ve had best luck hitting these places during lunch time or early evening (6 p.m.-ish), although Lem’s will quite often have ribs just coming off the smoker fairly late into the night.