Yellowstone-Canyon Village & Fishing Bridge

As you already stated, Fishing Bridge is a parking lot with trees. Very tight campsites. We barely had room to extend our awning and the tow vehicle had to be parked across the site instead of head in.
But we didn't spend any time there anyway because we were out with the 1,000's of others in the various traffic jams throughout the park. One backup due to a bear sighting was over 5 miles long.
Yellowstone is one of my least favorite national parks. Too crowded. We left there and went to the Greys River southwest of Jackson Hole. There is over 60 miles of river and road without a single electric pole and that doesn't count the 100's of miles of side roads. Probably saw no more than a dozen other vehicles during our 3-4 days on the Greys River. There are several National Forest campgrounds along the way with vault toilets and if I recall correctly several had hand pump water.

We stayed in Fishing Bridge when we went a few years ago on our first trip. If we were to go again, I'd pick Canyon Village even though it has no hookups. As you expect, we spent very little time in our camper, and I think Canyon Village has a nice central location. Fishing Bridge is handy because of the hookups, but since we spent so little time there, we really didn't need them. It was so chilly at night (down to 32 in July!), there was no need for AC either.

They are both well-located, fairly close together.. you can tour the north part of the park from Canyon and the southern part from FB.

FB is so often described on this forum as a parking lot and it is true that it is paved. But I was surprised at how many trees surround it. Deer and Bison strolled through. It's not a wilderness disbursed camping environment, but is actually a nicer setting than some NP campgrounds we've seen.

Enjoy!