I can't help with campgrounds, but the number of days you will be there will be enough. You can't go to Yellowstone w/out seeing the Guysers, Hot Spots, Old Faithful, Mammoth Hot Springs, the falls. All of those areas will be busy tourist areas, but I would not miss them. You will need your car because Yellowston is so massive. I would recommend stopping at the Visitor Center watch the movie and talk to the rangers. If you want to get away from the tourists, hike the trails. If you are hiking in the northern regions, I would make certain to carry a bear spray canister and know how to use it. The beauty and wildlife of Yellowstone will create memories that you will carry forever. We have been there 3 times, plan many more trips. Yellowstone can be tranquil away from the tourists and it can give you a feeling of coming home each time you arrive.