If you have your own car or a rental, you can easily drive from Athens to Metochi—an area located directly opposite Hydra—in about 2 hours and 45 minutes.
Following Attiki Odos and then the Athens-Corinth National Road, immediately after the Isthmus, take Exit 10 (Corinth - Epidaurus). Turn left under the bridge onto the road leading to Loutra Oraias Elenis and continue toward Epidaurus.
Drive for about 45 minutes until you reach the Epidaurus junction. Shortly before, you will see signs for Poros or Spetses. At the junction, go right and then immediately left under the bridge.
Further down, at another junction, bear left at the sign indicating "To Poros." Following the coastal road, you will reach Galatas (opposite Poros) in about 35 minutes.
Cross through Galatas and continue along the same coastal road. You will pass through the areas of Plaka - Lemonodassos - Aliki, and after approximately 35 minutes, you will arrive at Metochi.
The road is quite good, and the total trip from Athens to Metochi at an average speed takes about 2 hours and 45 minutes.