Yes, there is few hotels nearby, just some guest houses which can only be booked on arrival. you may have to entrust a travel agent in Beijing to help reserve the room for you.

you can also stay at the wall over night.
no need for a hotel. take some candles, sleeping bag, water and food.
but don't forget money! there are some locals who charge you two yuan each for passing their land and using their ladder or so.
in any case it is a great experience. i did it 5 times in the last 10 years and it's always amazing. i can only suggest it!

Is it also possible in Jinshanling?