Το μοναστήρι στο βουνό means that the monastery is somewhere at the mountain, propably on the mountain, maybe in the mountain. In greek, thanks to the accusative case, you don't always have to use a preposition. So, στο βουνό can be either on the mountain, at the mountain, in the mountain etc. If you feel like specifing exactly where on the mountain, then you can use a preposition. το μοναστήρι είναι πάνω/ψηλά/μέσα/κτλ στο βουνό= the monastery is on/way up/in/etc the mountain.
Thanks. I tried "at the mountain," since I didn't think it could be on without πανω and I didn't think cave monasteries were common enough for it to be "in the mountain."
You are right about that. All of those prepositions should be accepted. They are now ;) Thanks for the input!