In the cliffs neighbouring Persepolis are two ancient sites featuring rock-hewn tombs that are well worth a visit. Naqsh-e Rajab is the closest to Persepolis but Naqsh-e Rostam is the more spectacular of the two sites.
Most tours to Persepolis also stop at Naqsh-e Rostam and Naqsh-e Rajab. It's feasible to walk the 6km from Persepolis to Naqsh-e Rostam, stopping off at Naqsh-e Rajab en route in winter but this is not an option in the heat of summer. Alternatively, a round trip in a taxi dar bast from Persepolis costs IR500,000 including waiting time.