Perhaps others can chime in with more knowledge, but I think a cab might be your best bet. We drove there, and it didn't seem to be near much of anything - the entrance is on the side of a switchback road outside of the city. It is a very cool site, though.
Is it worth visiting?
It is definitely an interesting site -- a massive tunnel through the mountain ending in an amphitheater with incredible views. I guess if it is worth it depends on how much time and hassle it might take to get there. We also really loved the Flavian Amphitheater, which is probably easier to get to by public transport -- walkable from a metro stop, I believe. While smaller than the Roman Colosseum, it was more fun because you could freely wander the underground area. There are some photos of both attached to my review of the tour company we visited both sites with: https:/…REVIEWS