Yeah if you want fine BBQ , Memphis is it, But if you want the world best tasting BBQ, Kansas City is the place to go. Where there are almost 100 BBQ joints in town. Everyone has their own favorite place. Here a small list of some of top choices..
Gate's and Sons
I'm sure you will find after having Kansas City's BBQ you will never want anything else.
In Memphis (where most, if not all, of the finest BBQ in the world is to be found), you could start with: Cozy Corner, Germantown Commissary, Corky's, Interstate, Rendezvous.... hmmm.... getting hungry just typing this, since I don't live in Memphis any more.... Memphis 'hounds, additions or corrections?