The Franklin/Cool Springs area is definitely a 'nice part' of town. East Nashville is supposedly gentrifying with young people. You should be able to find some pretty nice exurbs with land for horses but still easily accessible to Nashville or Franklin (which is just 15 minutes south of Nashville on 65.) I don't know a lot of the specific names of neighborhoods within the city, but for the most part I get the idea that Nashville is not too rough and tumble overall. It certainly is nothing like Atlanta.
I never lived there, only visited often when I lived in Knoxville, but traffic seemed somewhat irritating at worst, but not usually a daily gridlock.
I think that Nashville on the whole, is awesome. There is plenty to do, a walkable downtown area, huge live music scene that isn't just country, a growing number of breweries if that interests you.