You can pay extra money to see the Karanlik Kilise (Dark Church), which is a cave church with exquisitely preserved frescoes, and worth the admission fee. The paintings are mostly biblical, and might be tough to understand without a guide, but there are enough around that you should be able to just listen in on one.
There is a cafeteria at the entrance to the museum (of course). The site itself doesn’t take that long to walk around, but give yourself some time to explore everything. A few hours should be enough.