I have driven to Naufplion and from there to Mycenae numerous times and its not as hard to find as is Ancient Olympia which was annoying, plus a lot farther.
I take the old 2 lane road, which you turn onto just before entering Corinth from Athens, instead of the new toll highway, as its much more scenic, has less traffic and all you have to watch out for are the occasional herd of sheep or goats blocking the winding road.
You also get to drive through the Greek wine producing region of Nemea, so be sure to stop at the roadside stands for some wine to take along but not to drink and drive with. Locals in Datsun or Mazda pick-up trucks breeze through the stop signs at RR crossings but I at least slow down to save my suspension.
Trains are rare but do ply the route. Public KTEL Bus will work too but not to the site of Mycenae itself.
Wear your sensible shoes for all these ancient sites. Its rocky!! I actually saw one girl at Mycenae with teenie backless sandals crawl all over the site with no problem but she was a regular Maenad. My sneakers were fine. But bring a sweater too, as being in the gully between high hills, and early in the morning when you might arrive, the sun wont warm you much in the wind at the top of the acropolis! When you take the tour you have a choice between A class and B class hotels and the B class is in the center of town so you have more options at night and its even cheaper. The A class is pretty decent however too!
I was there recently and it was so windy you could hardly stand up and its exposed too. I am not exaggerating it was gale force. There are some fairly serious inclines to be negotiated here how ever they have built new ramps and they seem quite sturdy. Others times it was far less windy but wind is nothing to be surprised at in Greece! A wind breaker, hat and sunglasses are always a good thing to have in your day pack!