From Butte, the best route, direct, would be I-90 to 287 and down through Ennis and to West Yellowstone. Yellowstone is huge, but Grant Teton not as much, just spread out more. You could home base in West Yellowstone giving you a direct route through YNP to GTNP and back. Then use your other days to travel the other parts of YNP. You could do all your exploring of YNP from West Yellowstone, then move to Colter Bay RV park or CG and explore GTNP from there. I wouldn't recommend Gros Ventre CG. It was recently expanded and sites are practically on top of one another. We saw huge Class A's in there but how they got in there is a quandary. When we go, we either stay in West Yellowstone at Baker's Hole FS CG (has electricity at most sites), Grizzly RV, or the KOA, or we stay off the Togwotee Pass in WY at Falls CG. We have stayed at Henry's Lake and Red Rock RV park on the Idaho side and have driven in as well. There are a lot of options so be open for another busy year of RV'ing with this Covid19.
