With your desire to go somewhere warm and also perhaps also to do a cruise I think Florida is your best bet since you start from Nashville.
Just arbitrarily picking Orlando as a base in Florida and cruising out of Port Canaveral your total miles round trip would be 1500 with about $300 for fuel.
That assumes you get 10 miles to the gallon with gas costing you $2 a gallon.
Now if you went to Texas deep down in the Rio Grande Valley at Mission where it is warm you would have to cruise out of Galveston which is way north (400 miles) so your total miles down and back including cruising would be 3000 with a fuel cost of $600.
Of course if you went down to the Mission Texas area you could do your cruise on the way down there or when going back north which would save you an 800 mile round trip. Texas is a big state. Remember, it is 400 miles up to Galveston if you are already down in the Mission Texas area.
If you would decide on Arizona then Yuma is your best bet. You could then cruise out of San Diego. The total miles in that case would be 4000 with a fuel cost of $800.
Now Orlando is sort of the breakpoint in Florida where above that it is a little bit colder and below that it becomes much warmer so you would have to adjust your location in Florida based on whether you want toasty warm all the time or you can put up with some chilly mornings farther north where your camping cost would be much cheaper.
Of course you're camping cost in Florida will be a lot higher than Arizona or Texas but if you look around carefully there are deals especially if you can stay farther north. And the cruise opportunities out of Florida are vastly better than Galveston or San Diego.
I hope this helps you a bit with your decision making process. And half the fun is in the planning they say.