Private Peloponnese tour?

Rick Steves recommends several guides for Greece. This link may be helpful: https://community.ricksteves.com/travel-forum/greece/mycenae-tourguide When we took the RS Greece Tour all of our local guides were knowledgeable and engaging.

Depends on your comfort level but renting a car is very easy (and driving in Greece, although some here find it a little more challenging than what we are used to in the US), and its very easy to self-tour the sites you mention, and that is my personal preference (but again, depends on yours). It is easy to use a guidebook to see the sites, and getting there from Nafplio is very easy. I think that few people ho visit Greece speak Greek - you will be fine without Greek. I prefer to be on my own schedule and have the freedom and flexibility of a car. Fwiw, we used Athens Car Rental, which we picked up at the airport and drove from there to Nafplio. Some here dont recommend this after a long flight bit we felt comfortable and it was fine. I would not drive in Athens itself. Drop the car when you get there

Thank you, Janis and Jessica.

Our experience is pretty much the same as already posted.
English is spoken by virtually every Greek under 60.
We too used Athens Car Rental ACR. Arrange to meet them at the airport. The drop off the car at arrivals. You do a walk around to note damage. Its a good idea to video the car. I missed a dent but my wife videoed the car and the dent was on the video so we had no problem with the inspection when we returned the car. They do take a deposit for damages greater than the deductible on the insurance they provide. If there is no damage they don't put it through on you credit card .

The airport pick up is important because you can drive all the way to Corinth on a major highway. It is a toll road so have cash with you. Generally speaking the rental cars are small and a bit under powered. They are no match for the high powered vehicles the Greeks drive. It is customary for all vehicles to stay way over in the right lane to allow fast vehicles to pass on the left. These vehicles are probably going by at about 150 km/hour.
You mention crazy drivers. I can say the Greeks love to go fast and they also cut corners. There must be a Greek gene that causes them to drive over the centre line. They all do it. It can be a bit disconcerting to go around a corner and find a vehicle straddling the center line. They always manage to get back across safely. I bring this up because after Corinth you will be on rural two lane roads not super highways.

All the road signs on the roads are in Greek but about 200 meters further along there are signs in English. Its a good idea to have a paper map and or a GPS so you have no worries about getting lost.
Tourist driving in Greece requires the passenger to be alert and actively watching for signs and following the map. The driver has to have all attention on the car and the road.
I am telling you about this not to disturb you or to dissuade you from renting the car but rather to prepare you for the experience.

I might suggest that you make a stop in Corinth on the way to or from Nafplio . Don't go into the city, the traffic is crazy. You can easily visit the canal. There is a path that runs along side of the canal. There is a ww2 pill box, an abandoned rail line across the canal and a spot where the keels of the boats were dragged across before the canal was built. You can still see the deep scratches in the rock.
There are three additional sites nearby. Acrocorinth a mountain top fortress with 360 degree views. Right next door is ancient Corinth from the biblical Roman time and lastly Ancient Nemia. It was a sister city to Olympia and still has its stadium a partially restored temple and a very good museum. It takes about an hour to visit Nemia.

Here are some images
Corinth Area. https://www.flickr.com/photos/stanbr54/albums/72157711755443483
Nafplio https://www.flickr.com/photos/stanbr54/albums/72157632094108982

A half-and-half option would be -- head for the Kifissos Bus Terminal for the KTEL intercity bus service -- Busses are modern, reserved upholstered seating, A/C, prompt, take 2.5 hours... normal years hourly on the half-hour, may be only every 2 hours in May 2022. Have hotel res. for 2 days, & ask hotel to reserve a car for 2nd day. On 1st day explore gorgeous Old TOwn, walks, Acronaflio, Museums, sunset etc. On Day 2 leave early, do Mycenae, then Epidaurus, cap it off with a swim on the way back (Tolo or Assine). Next Day KTEL in AM back to Athens... If your tour covered Athens, then u can go straight to Airport...

My wife and I followed Rick's self-guided Peloponnese tour in 2018 using a rental car. This was our first time renting a car on a European trip and it went very well, just make sure you have a GPS and a good map as a backup. And, just in case, purchase all the additional insurance.

We easily self toured by rental car on the Peloponnesian Peninsula. Napflio is near many antiquities, easy to see by car. I can’t imagine taking a tour in such a relatively easy to drive place. You will be driving through beautiful olive groves in that area.
Signs will be in Greek and English. No worries! Pick up the car at Athens airport and take a regular highway to Napflio.
Stay several nights and tour the area.

We took the RS Greece tour and were very glad we did. I would not want to drive those challenging roads on the peninsula. And I have driven in Norway, Scotland and Ireland. The scenery is gorgeous so the driver would miss out. Also, having local guides to tell us about what we we were seeing was great.