I can't help you with Chattanooga, but have lived in Nashville for 15 years so can give you my opinions on our BBQ here. There are 3 in Nashville that I would recommend you trying. Martin's BBQ Joint. Martins has the best ribs in town and his brisket is very good. I'm not a huge fan of their pulled pork. He smokes whole hogs so you loose some of the bark on the pork. Also if you want something a little different than bbq there his burger is the best in town. He makes a brisket burger that is a burger with brisket on top and bbq sauce. I would recommend the burger or the big mama's sampler here. 3 locations but the Belmont Blvd one is the most central.
Peg Leg Porker. Only does pork and chicken. His pulled pork is better than Martin's but the ribs aren't quite as good. It's close to downtown in The Gulch. The Gambling stick. It's a trailer in a butcher's parking lot in East Nashville. They are usually only open Thurs-Sun, but sometimes they don't open Sun if they have been really busy and run out. There is a little picnic area to eat. Whatever you do, DO NOT GO TO JACK'S DOWNTOWN. IT IS AWFUL!. You have been warned.
