Not really. More like restaurants that also serve drinks. There's a place on State Street called 620 State that makes a smoked Old Fashioned that's pretty good. It's within walking distance of a BBQ place called Delta Blues. It's a hole-in-the-wall, tiny spot. But, their BBQ is good and you can get a combo plate with smoked jalapeno sausage (this sausage is really good). I'd hit the BBQ and then walk over to 620 for drinks.
I don't know what kind of experience you're looking for here, but if it's something like spring break lite, you won't find it in Bristol. Knoxville would definitely have more actual bars, and different classes of bars. Asheville is full of nut jobs, nudists, and hippies - they also have an unreal amount of local breweries and beers nobody else has ever even heard of.