I have responded on Tripadviser but am posting my reply here also.
Its good you have a van and driver which is really important because there is no way you could possibly start this trip driving while jet lagged.
Your Tripadviser post has a slightly different plan. Day 1 was Mycaenea and Nafplio, Day 2 was Epidavros and Nafplio and day 3 was Hydra.
With that plan my comments were: Day 1 and 2 are fine. Just enough activity allowing for some recovery time.
Day 3. You are doing a Peloponnese/Mani trip. Using a day to go to Hydra is a loss of focus. Nafplio feels like a Greek island because its on the seashore. Use your time in Nafplio as your island time.
Be sure that you find a hotel in Nafplio in the old town area. Its magical wandering around the old town particularly the main square in the evening.
While just on the edge of the old town look at Hotel Agamemnon. Its the only hotel right on the sea front by the waterfront promenade.
So back to day 3. This is when you want to drive to Sparti and Mystras. You need a minimum of 3 perhaps 4 hours to do Monemvassia. Have your driver take you to the top and work your way down. The driver will meet you at the bottom of the site. Be sure to bring snacks and water with you.
Drive to Monemvassia. You asked if anything you particularly enjoyed in Monemvasia?
Monemvassia is called the Gibralter of Greece. Its a massive rock formation on an island (joined by a causeway). It is a walled town and the moment you walk through the bullet scarred main gate you know you are experiencing something very special. The main street is cobblestone and just wide enough for two donkeys to pass. The hotels are actually restored period rooms in 14th century buildings spread out through the village. Your imagination will sore in Monemvassia.
Even our Greek friends love going there, one of them said when you are in Monemvassia you just want to play pirate.
The level above the village was a fortress. It was heavily bombed in ww2 but is still an impressive place. You will not regret dropping Hydra and adding a second day to Monemvassia.
Next day doing Dyros caves and down to Gerolimenas is doable.
For day 6 you do not have to return to Gerolimenas for the night. The Mani should be done as a circle route so you will follow the coast going north. Don't miss the abandoned tower house village of Vathey. We spent a good 2 hours wandering around this amazing place.
You should be able to spend that night in Githio or perhaps Sparti. This will mean you will have a much shorter drive back to Athens on your last day. I am going to suggest that you use that extra time to make a stop in Corinth on the way back. Corinth has some great sites including the canal, Ancient Corinth and the amazing Acrocorinth fortress with its 360 degree views.
We did a similar trip a couple of years ago.
This is what we saw
Corinth Area. https://www.flickr.com/photos/stanbr54/albums/72157711755443483
Peloponnese, Mani and Monemvassia. https://www.flickr.com/photos/stanbr54/albums/72157711323535897