Is there a great place to sleep on the mount?
There are limited hotels on the Mount and several of them are managed together. I stayed in the Hotel Croix Blanche while on a Rick Steves Tour there. It was fine. Lots and Lots of steps up a spiral staircase.
Almost all of the hotels on the island itself are owned or managed by the same company (the Poulard Group, you'll see their name everywhere). That being said, there is nothing like staying overnight on the Mont itself. It is worth the price and mediocre accommodations IMHO.
Sleeping on the Mont is all about three things:
Location
Location
and Location
The actual accommodations are not 5-star luxury. They are perfectly OK, comfortable enough, but more "historic & atmospheric" than fancy. Not really places that you would seek out of they were anywhere else, but they're fine for where they are.
The rooms on Mont St Michel are overpriced and will undoubtedly require a lot of climbing, either up the streets, up narrow staircases, or both. Yet, we have almost never been disappointed in our 5 stays on the Mont.
We’ve stayed twice at a room with a balcony at La Vielle Auberge. It’s about as high as you can get, way up on the Mont. Expensive, but the overview is worth it IMO.
We’ve stayed at le Mouton Blanc in a small but modern room with a sleeping loft for our granddaughters. Charming.
Twice, both times over a decade ago, we stayed in the annex of Le Mouton Blanc. Our first stay was fine. The second time, the door leading to the outside didn’t latch properly and it left me feeling uncomfortable. I understand that crime is virtually nonexistent on Mont St Michel, but if I had it to do over again, I’d check that door while there was still staff on duty at the Hotel/Restaurant.