I don't think those that have posted it is OK, and certainly those that suggested staying in West Yellowstone read your whole post. I would guess they were responding on just where to stay in Yellowstone.
IMO, the parks are too big to try to stay in one campground to see both parks. You will spend way too much time driving.
We are doing a trip this year, staying in Gros Ventre in Teton's, and Fishing Bridge in Yellowstone. I don't like the atmosphere of Fishing Bridge, but it is the most centrally located campground. And we won't spend much time in base camp.
