Very few people do it and I must admit that the view is a bit disappointing but by taking the staircase that goes to the right of the entrance of the cave, you can climb to the top of the mountain where there is a chedi. I am not convinced that the view rewards the effort of climbing the more than 600 steps but it is up to you.
Note that if you are hungry, in the parking lot, there are several food vendors and you can sit at a small terrace with a nice view over the valley. Oh yes, I almost forgot, there are monkeys living on this mountain. Personally, I mostly saw them at the parking lot but it is part of the assets of the place. I advise you to stop at the Muang On cave before going to San Kamphaeng Hot Springs, the cave is really impressive and like that you keep the relaxation for after visiting the cave. After the effort, the comfort as people say!