There is no airport in Mystras. The closest airport is located in Kalamata, the capital of Messenia. The airport of Kalamata is small and works only in summer. It receives domestic flights from Thessaloniki, not Athens.
In summer, it also receives charter and low-cost flights from Europe. In particular, the low-cost companies Easy Jet and Ryan Air operate flights to Kalamata.
Visitors can go from Kalamata to Mystras with rental car or bus (via Sparti).