There are daily buses from Athens to Mystras via Sparta. The bus from Sparta to Mystras also serves other villages in the region, like Trypi where the Keadas Cave is found. A very popular way to get around Mystras is also on foot as the region has many trekking paths and natural beauty.
A very convenient way of transport around Mystras is also by car. However, there are no car rentals in Mystras or Sparta, therefore you must have your private car or you must have rented a car from another place.