If you don't mind driving 30-40 miles, drop down to Colter Bay on Jackson Lake and "dry" camp at the campground. It's about 40 miles, more or less, from Colter Bay to the South entrance and about 20 miles past Lewis Canyon and Lake to get to the junction for Lake or Old Faithful. We do that quite a bit as we tow our FW and boat to Jackson Lake, park in Colter Bay Campground and fish. Then, if we are a little tired of fishing then we may go to Yellowstone for a day trip. It's not too bad, but folks on here will tell you to go to West Yellowstone because it's a shorter drive into the Park, and it is, but I don't think it's anymore convenient than Colter Bay. If Colter Bay is too far, might try for Grant Village, it's in the Park close to the junction I noted above and has "dry" camping on a first come/first served basis I believe. If you get there sometime mid-morning, you probably shouldn't have a problem getting a spot in August, same at Colter Bay.