We have visited three of the four Nabatean seetlements in the Negev mentioned, as well as others further south. The Negev is a sparsely populated arid region with limited public transport, so however you travel, you will need stout footwear and lots of water.
We went by car, but there are bus services from Beersheva to Avdat (Beersheva to Mizpe Ramon bus, then a long uphill hike), Mamshit (Beersheva to Dimona, then a 10 km walk or hitch from Dimona), and Shivta (Beersheva to Nizzana bus - twice daily, then a 8 km walk from the turn-off).
These three towns are in a good state of repair, being only around two thousand years old, and are not frequented by visitors much.
The Nabateans built the towns as a series of resting places for their caravans travelling from Egypt and Gaza to Petra and beyond. Some additions were made by the superceding Romans and Byzantines.