Feel free to hit me up if you want some first-hand knowledge of the area. Because if you were doing it, your best bet would be probably to base yourself somewhere like Nafplio and use the bus system or hire a car. (Bus stops at Tiryns and at Epidauros, but Mycenae is 3-5K from the bus stop and Argos is a complicated town and the bus goes nowhere near the fortress above the town.)

*helps like enthusiastic cats*