Mycenae Greece map
Coach tours are the easiest way to visit Mycenae Greece if you are staying in Athens or nearby. Most of them operate a full day tour, and also call at the site of Epidauros. (They usually fit in a rather long stop at a local pottery store, hoping you'll buy a few items and earn the tour leader some commission...) It's actually quite a good day out, as they usually stop at the Corinth canal for you to get some pictures.
You can also get to the site by taking the Athens to Nafplio bus which stops on the main road at the village of Fihtio. It's about 3km from the village, but don't forget the site is another 2km further.
Three buses go to the site from Nafplio each day. These buses stop in both the village and the ancient site. If you want to stay locally, there are a few small hotels in the village, but in high season they are usually fully booked.
You can see from the map that Tiryns is just 4km from Nafplio. Any of the buses which travel between Nauplion and Argos can stop just outside the site.
This area of Argos is full of ancient Greek places. If you're really keen on exploring the ancient sites, the most relaxing way to do it is to stay in Nafplio and hire a car. Nafplio is a gen of a resort town, and was for a brief while the capital of Greece in the early days of independence. It has many attractive tavernas and restaurants, and is a great place to relax after a day submerged in ancient history.
This map shows you where the site is in relation to Nafplio (just hover your mouse over the red markers). You can use the controls on the left to zoom in and out of the map, and you can move the map around by holding down your mouse button and moving the mouse around. The "Satellite" view isn't especially interesting as the resolution for the area isn't very detailed, but if you zoom in on the sites you can see the main features.