I first remember going to Mytoi with a very close friend about 10 years ago. We had a great time and said prayers from my Russian Orthodox Christian prayer book. I know that's not exactly zen meditation but the garden is a it's a great place to relax with quiet time or enjoy with friends and family as a social event. Also, do NOT neglect the paths across the road. They lead through the woods to a cove of sorts. The paths are quite a different experience than a Japanese garden but add a lot to a visit to Mytoi. The view of the cove is wonderful and the walk through the woods takes only about 20 minutes though you can linger longer if you wish.
When I returned to Mytoi last summer with my wife, toddler son and in-laws we had a GREAT time strolling the gardens and, as I said, we also GREATLY enjoyed the paths across the road which, as I understand it, are also open to the public.