I would stay in Riverton or Greybull and drive to Thermopolis. Only 3 RV parks in Thermopolis area and they don't get good reviews. The "best" one is Eagle RV Park. In Riverton we stayed at Wind River RV Park. Easy drive to Tetons from there. In Greybull we liked the KOA. I would call ahead for reservations and to make sure they know your rig size. Their sites are paved and level but some are tight if you have a toad. They served an awesome breakfast for a reasonable price the next morning! Greybull is a neat little town. For Cody we stayed at Yellowstone VAlley Inn RV Park between Cody and Yellowstone. We drove into Cody (18 miles) and drove to Yellowstone (30 miles) from there. Not a fancy park but had everything we needed.