Be prepared to sleep in the car. If you know anyone along the path, ask to sleep on their lawn or something. Start driving down probably a couple of days out. http://www.eclipse2017.org/2017/maps/whole-us.jpg
Flights New York - Nashville for Sunday - Tuesday (I didn't check Monday evening return flights) seem to go at a bit over $1000, and some still available hotels $300 to $1000 per night.
Could also check prices to fly to some other cities on the path in the map. Kansas City?
Beware that cloud cover also affects where you might want to go to view the eclipse. The West (basically Idaho, some of Wyoming) is looking good right now. You could fly from EWR to Idaho Falls round trip for less than $800. The airport is in the the middle of the totality zone so even if you can't find a car or accommodation you'll still see it. Also Jackson, WY but air fare is a bit more to there.
You probably won't get home Monday.