Agree with the suggestions to use a separate base camp for each Park. IMO Grant is too far south of the major points of interest in Yellowstone. The great majority of the thermal features are between Old Faithful and Madison Junction, and we prefer Madison campground for that reason. It's also not far to the Norris Geyser Basin and Yellowstone Canyon and the Falls. Canyon campground is also a good central location as is Fishing Bridge if you need hookups. The northern loop of the Park can be done in a long day trip from any of these.
For Grand Teton, our favorite campground is Gros Ventre at the southern end of the Park. Colter Bay campground, further north is good also. There is a FHU RV Park at Colter Bay as well.
