We were at Yellowstone in mid-June and stayed at Fishing Bridge CG. The spacing is close but not too tight. We have been in way tighter CGs (Pismo Coast Village).
We spent a lot of time driving back and forth to the main geyser/hot spot areas on the west side of the park. It took close to an hour to get to the Old Faithful area from Fishing Bridge via the road along Yellowstone Lake.
Many reviews say the park is less crowded in June than July. That may be true but it seemed very crowded even in June. It was more often than not we could not get a parking place in some of the main geothermal areas on the west side, usually having to wait in a traffic line just to circle the spaces waiting to get lucky.
If you want to do a lot of geyser viewing, you may want to consider Grizzly RV. But please take into account the line to get into the park each day. We didn't have to deal with this at Fishing Bridge however.
Then we were down in Jackson at the Virginian. It was a very nice and clean campground/RV park. I didn't not find the management rude in any way.