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Budget travelers: Ride the bus to the very top of the hill and stay at the hostel there. Great views. If you come in on the train from Roma, ask the information desk where the hostel on the hill is and they will tell you which bus to take.
There is a restaurant there at the top of the hill along the road across from the walking path. The restaurant has the best pesto gnocchi I have ever had. It is a mom-and-pop place and I cannot remember the name off hand.