I would suggest that you stay at Colter Bay, about 10 miles inside the Grand Teton Park entrance. Their "dry" campground has fresh water and two dump sites with three holes in the ground. Great shade and close to one of the prettiest parts of our United States, Jackson Lake and the Teton Mountain Range. Also, pretty centrally located for traveling in the Park, to Moran entrance or to Signal Mountain, Jenny Lake and out to Moose Entrance and the Craig Thomas Visitor Center and then on the the Moose/Wilson Road and the newest part of Grand Teton, the Lawrence Rockefeller Reserve that was the family getaway, but they moved out about thirty buildings and reclaimed the ground so you almost can't tell where any of the buildings were and it sits at Phelps Lake, I think that's the spelling, which is also very beautiful. If the water isn't too low on Jackson Lake at that time, you could take a cruise that takes you to the base of Mt. Moran for a wonderful "look up" view of a mountain rising about 6,000 feet right out of the lake. Also Jenny Lake has a cruise to a place called Hidden Falls which is very pretty as well, although you can hike to the falls from the visitor center if you like, it's pretty easy. You notice, I haven't said much about Yellowstone, it speaks for itself and is a wondrous place with lots of ground to cover and features to see. We always take a day or two, while in Grand Teton, to go to Yellowstone and see as many features as we can. If you stay in Yellowstone for a week, you will get the chance to see almost all of the easily accessible features and probably will be able to hike to some of the less accessible ones. Just remember, it's a really big piece of real estate. In 1988, the fire burned 1,000,000 acres which was just about 1/3 of the total park area. That's over 1,500 square miles. Most of the burned area has now mostly recovered with tons of trees and undergrowth, but you can still see a huge number of burned trees and ground. And, right now they have, I think, three fires burning in Yellowstone in remote areas.
Have a great trip, if you would like some pictures, send me a private message with your email address and I would be happy to send you some.
John A. Lichty