A good 1/3rd of your trip stopping point is at Natural Bridge Campground in Virginia just off of I-81. Not sure where you're leaving from, but I'd say it's a good 8-9 hours which is a good day's drive from NY. (Another 8-9 hours to GA from here as well). It's a beutiful campground where you can camp right next to a river. You will have to contact them to find out if they'll still be open, I know the KOA campground there at natural bridge is open all year round, and serve dinner nightly all year round. Anyway, here's the link to the area, you might have to do some digging for the info on the campground tho. They do have a lot of info on the KOA campground and can be searched out by their web site.
http://www.naturalbridgeva.com/index.html
This is about 1.5 hours from my house btw, and if you're travelling down I-81, you'll pass within about 10 miles of my house if you were curious. Anyway, hope this helps!
[glow=red,2,300]Happytrails..........[/glow]