The location of H Basiliani is absolutely stunning, on the side of the gorge, in the middle of Matera's sassi area. There are cave dwellings (some renovated, some not) either side of the hotel buildings, and the breakfast terrace and some of the rooms (including ours) have panoramic views across the gorge at older caves on the other side. Our room was very large (split level, obviously meant for a family rather than just the two of us!), calm and comfortable. My only criticism is that the bathroom was about due for another coat of paint. Because the hotel is in the historic area, you cannot drive to it. You need to leave your car somewhere in the modern part of town (the hotel can advise on a choice of car-parks), and then call the hotel, who send their shuttle to collect you and your luggage. They also offered to shuttle us back to our car if we wanted to go out for the day, but there is enough in Matera (within walking/climbing distance) to keep you busy for a couple of days, so we didn't bother. I have read complaints about people waiting for the shuttle - this is only a small hotel, so there are only one or two vehicles - as long as you know there might be a wait, I don't see this as an issue. Staff were very friendly and helpful, and I can't think of a better location to stay in Matera!
If this is your first visit to Matera, bring a satnav or a decent map. The street signs in the modern town are dreadful, and we spent nearly an hour driving round completely lost.