There is no airport in Mycenae. The closest airport is located in Athens, the capital of Greece. The airport of Athens operates domestic flights from most Greek airports and also many international flights.
To go from Athens to Mycenae, you can go by rental car or bus (via Argos or Nafplion). You get the bus to Mycenae from Kifissos KTEL Bus Station in Athens. The bus trip to Mycenae is 1 hour and a half.