J.E.
We were in Yellowstone in 2000, just my DH and I. We camped in a tent, so I can't recommend any cabins. However, I can recommend that you stay on the side of the park that is near the Grand Tetons. There was a big fire in the late 80s and much of the forest in Yellowstone burned. That portion of the park looks like a bunch of telephone poles (burnt up tree trunks) surrounded by new growth (very small trees). The rest of the park was beautiful, but there was another big fire shortly after we left which we heard burned up part of the pretty forest that was left. However, the Grand Tetons were GORGEOUS with great hikes, beautiful waterfalls and it's very, very close to Yellowstone. Now, I'm not telling you to skip Yellowstone because it has some unique characteristics you can't find anywhere else. Old Faithful is cool - and there are other geysers that are even more impressive that go off less frequently. All the hydrothermal stuff is amazing.
Have a great time!!!