Not far from Kamianets-Podilskyi is the area called Bakota. It's located on the territory of the Podilsky Tovtry National Park. The area is gorgeous and offers wonderful views from the top. Recently Bakota has become a mecca for tolkienists and followers of many exotic religions.
You can go down to the cave monastery of XI-XIV centuries. We were wearing shorts and the weather was too hot, so we didn't go. It's possible to collect water at the source near the monastery.
Getting there: Only by car. From Kamianets-Podilskyi drive to the Hrushka village, after which turn right near the pointer to the monastery. Then drive along the gravel road and follow the signs up to the cliff.