Sounds like you're travelling the "Lincoln Highway"  Lotsa stuff about that
on the web. Out west so to speak, there is plenty of Bureau of Land
Manglement land that belongs to YOU!  Treat it gently, leave em open if
they're open, closed if they're closed and consider whether you think that
"Livestock grazing on public lands are fare (sp) game" when foraging for the
evening meal.  Free camping at Spencer Hot springs,  Baker creek just out of
town towards the park.  No I won't give you the details it'd spoil all the
fun of finding new places.  There is a Yahoo group about free campgrounds,
too.

try not to trip on the trip.