My son and his family live in St. Augustine, FL and we visit them sometimes three times a year. One of the best trips was the one where we drove, delivering a car. My wife reminds me that it was good because it was only one way. We saw country that we have never seen before and likely will never see again.
I use this as an example of Kitfox flying vs. other means of transportation. If time was no issue. Flying my Model IV would be a no brainer. Low and slow has to be the best way to enjoy the country and meet the people. I think I would Use maybe two full tank legs per day weather permitting and find lodging afternoon and evenings. Better yet, find a buddy that will fly along side - can't beat a group flight.
One of our Arizona pioneers flew all over the country and into Canada in his Safari putting almost a thousand hours on his airplane the first year. With the group I flew with, we sometimes camped, but mostly Hotelled it. Pack light, but with contingencies in mind. I still scan for ultralight camping gear. My tent weighs four pounds and my 20 degree sleeping bag weighs under two lbs. and packs smaller than a football. Use laundromats. It can become fatiguing so there will be ample time on the ground for domestic chores.