My wife and I live in NW FL and we traveled basically the same route as Tiger1959 a couple of years ago. I agree with his choice of route. We saw the campground he mentioned in Yellowstone but were unable to stay because we waited too late to make reservations. Reserve now!!!
We had to stay outside Yellowstone because of our waiting to book a spot. The campground he mentioned looked wonderful! We entered Yellowstone from the SOUTH gate, Jackson Hole, and toured that "side" for a day.
Before entering Yellowstone we toured the Tetons....LOVED the Tetons! We spent 3 days inside Yellowstone and would have spent MORE, if we had the time. We used our Toad to tour.
We suggest exiting the park from the EAST gate and agree with Teddy Roosevelt, who said, "The 30 miles between there and Cody, WY are the most scenic and beautiful of all locations in the world!"
We also suggest spending a day in Cody and making a stop at their "world class" western museum, the Bill Cody Museum. You could spend two days alone inside it! An amazing museum for such a small town! Food at Irma's Hotel was wonderful! Breathtaking trip, to say the least!