Should be no more than 3 tanks of gas each way. Thats what it took me from that area when I used to drive from MA. Stop in NJ near the end of the turnpike, one in NC around Roanoke Rapids, one in SC around Waltersboro and one in Daytona. That was with a pickup that got around 21MPG. If your car does better than that, you will probably only need 2 tanks each way.
From Durham, NC now, I can do it in my full size 4x4 pickup in 2 tanks.