If you need to live on the mountain, it is recommended to live near Taiyangguan Peak near Yuhuang Peak, which is the best place to watch the sunrise. You can watch the sunrise when you get up and go out, so you don't have to climb mountains. There are Bayi Hotel and Sun Peak Hotel of the Air Force on Sun Peak, both of which are not expensive. Probably only a fraction of the price you want.
The water on the mountain is precious, so it may be troublesome to take a bath. You should be prepared for the local hotel conditions.
There is also a radio and television hotel on the top of the mountain, but it is not recommended to stay, because it is a high-power radio station with too much radiation and is unhealthy.
Hotels on the mountain, including those near Nantianmen and Tianjie, are more suitable than hotels, and the conditions are more general. Limited by conditions, it is impossible to have a star-rated hotel that is too advanced.
In addition, due to the influence of weather, including clear clouds, it is often impossible to see a perfect sunrise. I stayed at the top of Mount Tai and didn't see the sunrise. Although it is sunny, the sun is rising under the influence of clouds. When I saw it, the sun was completely out.
So be prepared, you may be disappointed.