I lean towards Gates extra spicy for sauce, Oklahoma Joe's for Ribs, Jack Stack for Burnt Ends, Beans and Creamy corn, and Arthur Bryant's for sandwich meat.
Oklahoma joes for certain. Best BBQ sandwiches. Their burnt end plate is tasty but I make better burnt ends at home... Just not enough bark on them. Gates is ok. I've heard Bates City BBQ is very good but I haven't been there yet.
Definitely OKJoes for a pulled pork sandwich (Jumbo). Jack stack has a great "po russ" (burnt end sandwich), and fiorella's smokestack (subsidiary of jack stack?) has great food, too. And if you go to jack stack, be sure to try the cheesy corn!