I've done my share of meandering around those parts of the country. I often have a planned route and reservations but not always. When I don't. I'll usually do some research on appealing options in the general area where I think I'll be roaming. I especially check for sporting events, local festivals, county fairs, etc that might make finding a first-come-first-served campsite hard to find. I almost never stay in private campgrounds and never again in Federal. The real gems I've found are county and municipal.
If you do that and don't mind improvising when things don't work out (i.e.: Walmart, Flying J) it can be done.