To get started, you could take this entire year hitting just the State Parks in Ohio.
Really, if you have the rest of your life, drive 50 miles, find a campground and stop. Stay a week and then move another 50 miles.
From Ohio, I think I'd head toward the New England area, then come down the Eastern Sea Board, work my way down to Southern Florida (Atlantic Ocean side), and then come back north on the Gulf side. Follow the Appalachian Mountains back North and head over toward Michigan, come around upper Michigan and then turn South again following the Mississippi. Once you hit the Gulf of Mexico again, head west a couple hundred miles and head North again. Head toward Montana then cut over toward Washington State and turn South via California. Go South to Mexico. This should take you about 5 or 6 years. Go North during the Summer, go South during the winter and keep zig-zagging across the country. Time is no limit.
LOL..... Sounds like fun but I don't think I can talk Momma into that one. :)