So while living in Nashville for 3+ years, I never found barbeque worth driving out of your way for, certainly if you're only going to be in town for a night or to. For whatever reason central TN is a barbeque gap between Carolina and Memphis and neither style penetrated well enough to create a noteworthy place.
The hot chicken thing, though...
Prince's absolutely, utterly worth every bit of hype it's gotten. Order one spice level down from what you'd 'think' you'd get--even if you which it was a bit spicier it will still be some of the best fried chicken you'll ever eat. Bolton's is also good, though less spicy, and Hattie B's get's a lot of love--but I'd posit that's half due to location. The chicken is good, but it's in a much nicer part of town (which is more convenient for your average yelper, let's say) and they serve beer. If you are making time for one, go to Prince's. If you are right by one of the others, drop in there, too.
As far as real restaurants in Nashville, I'd steer you to either Rolf and Daughters or City House, both in Germantown. Husk is supposed to be great, but there's a location in Charleston and so you've got more chances to eat at one.
Rolf and Daughters is not particularly southern inflected, but I've had some of the best meals I've ever eaten, anywhere, at RAD. Phil is a genius with pasta and his small plates (the larger ones are good, but not quite as mindblowing). Most things that can be made in house are, with a degree of execution that I don't see often, even in NYC. Good winelist, too, and great cocktails.
City House was the first of what I'd describe as the current wave of modern Nashville restaurants to open. Southern Italian+American South. Tandy Wilson worked at A16 during the Nate Appleman era and internalized a lot of that approach to cooking. Wood fired oven, creative pizza with a southern bent (if you get one of the greens pizzas, which you should, put an egg on it). The wines are all either Italian or American, with a Disorderly bent on the American wines, at least (the Italian stuff is hit-or-miss). Lots of Broc wines, especially, because they've been available in Nashville for a while and City House was an early supporter.
I'd stay away from Catbird--they've lost a lot of people and although the food and setting are cool (sushi style counter seating, but with hyper-modern food) the food isn't unique enough that I'd waste my only night in town on it.
Not that you'll have time for it, but I'll add that the best papusas I've ever eaten are ~30 minutes outside the city and dwarf anything in the DC area for quality.
Hope that helps!