I like to focus on the practicalities of reaching this rather remote WHS by public transport. It is not too difficult. Buses go from either Dodoma or Arusha, and they leave early in the morning in either direction for a couple of dollars. Shabiby is by far the best. Dodoma is about an hour closer than Arusha to the Kondoa rock art sites. The visitor center is actually in Kolo, right on the main road, and this is the place where you have to get off the bus, register and pay your fees. About USD 13 for the guide who accompanies you, and we also paid about USD 21 for 3 motorbikes bringing us on a rough road to the foot of the hill where the caves are located. We chose the B group consisting of 3 caves, about 90 minutes walk uphill and down again. I was told that normally it is possible to rent a car from the visitors centre, but that it was in repair during our visit. There is also an entrance fee. The main headache was to catch an onwards transportation from Kolo as most long distance buses have passed already in the afternoon, and we had to wait almost an hour, but then found a smaller local bus all the way to Arusha. 
Babati would be an option to sleep in case there are no more buses, but this is highly unlikely. We reached Arusha before sunset after about 7 hours on the bus from Dodoma.