The Virginian, in Jackson, Wyoming, is about 35 miles from the south entrance to Grand Teton at Moran. It's about 20 miles from the entrance at Moose, but you still have to travel from Moose to the Jackson Lake junction, about 25 more miles. Colter Bay has a pretty nice FHU park that has had a full sign every time we have driven by it in the last 20 years or so, so you need to get reservations if you want to go there. Flagg Ranch has a campground, don't know if it's FHU or not, but it's between Grand Teton and Yellowstone about three or so miles from the south entrance to Yellowstone. You might try them as well, as this would give you fairly nice access to both Yellowstone and Grand Teton. Remember, those miles you are traveling are full of places to see wildlife and some of the most gorgeous scenery in the country. Fishing Bridge is clear on the outside of the park by Yellowstone Lake and is quite a ways from a lot of the scenery and features, but would also be a great place to park while you are in Yellowstone. If you don't necessarily need FHU, Colter Bay and Gros Ventre have wonderful campgrounds as do Grant Village and Bridge Bay. And, don't worry about being too close to your neighbors, you shouldn't be in the campgrounds very much during your trip to the two parks as you should be sightseeing most of the time. Pack lunches for your trips and you won't have to worry about paying exorbitant prices at the eateries in the parks.