Born and raised in Nashville, though I've lived in Texas the last few years. Franklin and Brentwood are the most established, affluent "outside the loop" communities for white collar families. If you're willing to go a little further south Spring Hill is still close to Nashville but you can get a lot more bang for your buck. on the NE side Goodlettsville and Hendersonville are older communities that have seen a renaissance lately due to people looking to be outside of Nashville proper but still close. Same could be said fro Bellevue and Kinsgston Springs on the West side. I grew up in East Nashville, right down Main street from downtown. I love that city and would love to move back one day. I've spent countless hours on Friday and Saturday nights playing all the Broadway clubs, good times.
Climate is accurate to what others have said, you'll get all 4 seasons. Plenty hot/humid in the summer, beautiful falls, cold winter with some winter precip and a beautiful spring. Also absolutely gorgeous geography. Hills, trees, tons of lakes. Great hiking, fishing, camping etc.
One of the things that people rarely mention is how close you are to so many other places. you're within a few hours of St Louis, Atlanta, Memphis, Knoxville/Gatlinburg, Birmingham, Cincinnati etc...easy to take a day/overnight trip and see a new city.
Also, crazy good food town and some of the best BBQ around.
I'll be there in December and can't wait to eat at all my spots!!