When traveling with the grandchildren in a 30 foot motorhome, I had no difficulty finding places to stop every hour or two so they could work off some energy. Parks worked quite well from age three until the early teens, after which I started to have to look for places with some intellectual interest as well, like local museums or historic sites. For teen girls, a stop at a mall usually works, but these tend to be longer stops.
Across most of the country there will be small towns 15 to 50 miles apart, and almost all of the towns have parks. Most of the small town parks have adequate open parking for RVs towing or being towed, most of the day. Only occasionally would I encounter an "event" going on in a small town that tied up all the parking around a park or recreation area.
You have to get off the Interstate to find the parks, because the Interstate system intentionally bypasses all of these places of minor congestion (then runs right through the middle of the really big cities). Most of the time, the towns are on the old highways that the Interstate replaced, often serving as a business route. The problem will be not knowing whether something is there that makes it worth your while to divert into town, the Interstate guides tend to focus on what is immediately at the exit.
I find the parks most of the time by just traveling the pre-Interstate highways.
