Here is a list of campgrounds outside of Yellowstone, if you scroll down, you will find the South entrance, and distance to the entrance. Options are pretty limited, as other posters have noted, Flagg Ranch is close, but expensive (as is pretty much everything in the area, especially private CGs), the forest service campgrounds are generally better suited to smaller campers than 35' and have no services, plus many are closer to GT than Yellowstone. Inside the park options have been covered by other posters.
The OP hasn't mentioned what kind of amenities they want, or hookups, which further limits options.