We have stayed at a few places in the Hill Country, near Fredericksburg. They were nice and did one night stays. Not sure if that's too far away, though. The KOAs we've stayed at across TX have always been good with single nights. Last resort is always a Wal-Mart parking lot. They are free and it's ok with them to stay overnight, just not longer. You can even use their bathrooms, if need be.