Where to stay and helpful tips - Mont St. Michel

You can stay on the island. We did not. We stayed in a motel about a mile from the MSM shuttle parking lot. We arrived at about 4, drove to MSM parking and took pictures during "golden hour". Next morning we arriving at the parking lot at about 8. Took the shuttle to the island, walked up to the abbey and purchased tickets and were one of the first in at 9am. We did everything we wanted and left by noon. We didn't feel a tour was necessary. We used info in RS guide.

You could search the forum for opinions and info from others. There are always a lot of posts on MSM

There are always a lot of posts on MSM

This is true. Do a search. For me, there is nothing like staying on the island overnight (I have stayed both on and off the island). To say it is "magical" is trite but true. I suspect people that say it is "just as good" to stay off island have never actually stayed on the island themselves. YMMV. Keep in mind that almost all hotels and restaurants on the island are own by the same business: The Poulard Group (i.e., Eric Vannier). So there isn't any real competition. But just being there after hours to wander the lanes, ramparts and back alleys is like no other place on Earth.

It is nice in the evening on the island. You can do that without staying on it, but for people that like the accommodations and have the budget which it sounds like OP does, go for it.

Be forewarned, the worst food I've ever had in France and in the top five worst meals in Europe was what we had when we visited MSM. It was at one of the restaurants on the road leading to the abbey. The place we stayed just a couple miles off the island had a restaurant that was filled diners and with folks waiting. We wished that we had eaten there.

tlee,
Yes, food on the island is just so-so, in my opinion. Definitely overpriced! Known for omelets there, but I have had better elsewhere in France. When we were last there, we walked up the back side, behind the abbey. I don't know if that entry is still open, but it sure was less crowded. We descended by way of the main street. If possible, go up the back way (to the left as you face the entrance)

I agree with PharmerPhil
To say it is "magical" is trite but true
I would definitely recommend spending the night on the island.
I don't think you need more than one night. There is no admission charge for the island itself, but you have to pay for parking and for entry to the Abbey. Going into the Abbey is definitely worthwhile, even moreso to see the the nightly spectacles which are staged during tourist season (probably going on during your dates). I've never taken a tour in the Abbey so I can't comment on that.
The general consensus seems to be that the best times are when the island is less crowded, before the day trippers arrive (say before 9:30) and after they leave (from about 4:30 on). Personally, I don't find the crowds objectionable. Sure, they make it slower to walk up the one street, but the crowds are part of the experience. They are in addition to - not in competition with - the quieter times, which you will still get if you stay on the island.
In addition to the shop-lined, people-filled main (read "only") street, Mont St Michel is full of narrow passageways and staircases which make it fun to explore. Keep in mind that virtually every other step is going to be either up or down. I'm an old guy so I need to rest on the walk up to the Abbey.
A lot of the hotel rooms are located right along the one street. Try to get a room that does not look right out on the street. It can be noisy quite early when garbage is being carted away and stores/restaurants are being re-stocked.
One hotel, La Vieille Auberge, has four rooms high up on the island (just below the Abbey) which each have a private terrace. A little more expensive than other rooms (might be within or close to your budget) but it's a delight to sit on your terrace and look down over the town. For us, it's worth a splurge.

I am staying the night, though logistically it is difficult. You can’t bring a big suitcase so you either have to chance leaving it in the car or, in my case, leaving it at my previous hotel, although that would add a lot of driving time the next day. No AC, the reviews uniformly say no matter which hotel/restaurant, service is bad. Etc. But it just seems like one of those things you have to do once. I booked a room with a bay view.

Based on the food situation, I might choose a late lunch and then hope we can bring or find snacks.