Peloponnese tips please

It would be helpful to know exactly WHEN this trip is ... and what experiences are your priorities. Are you energetic hikers, climbers or less active. Are you ancient history buffs, byzantine stuff or more about scenery and dining or all of the above? Are beaches important? Before we spend time on describing our favorites, tell us more, to avoid wasted effort on what may be irrelevant.

Thank you,
I would say all of the above...we enjoy new experiences, love the outdoors-hiking, walking, great meals, also interested in history, enjoy everything about travel. Probably less interested in relaxing on beaches or swimming.

The trip is end of May/early June.

One of my favorite trips was very similar. The Bradt Guide is excellent and will hook you up.
Nafplio: Nemea, Epidaurus, Mycene
I skipped Monemvasia.
I did not make it to Pylos but I know there's beautiful coastline, a fortress
En route may be the time to visit Messene (highly recommended!). Make sure you work in a stop at Mystras
I stayed in Zatouna, the next town over from Dimitsana, the hike to the monastery is lovely. It's an easy drive back to ATH from there.
We found the driving easy and the scenery spectacular. Were also there in late May and we practically had some places to ourselves.

On the way to Nafplio stop at Corinth. You can visit the canal, consider a short hike along the west side of the canal. There is what looks like a machine gun nest, an abandoned rail line an the rail bridge over the canal and on a rocky incline you can see the scratches of the boat Keels when the y had to drag boats across before the canal was finished.

Also you may want to visit Ancient Corinth (biblical period) and right beside it one of my favourite things a drive up Fortress at Acro Corinth. It may be my favourite fortress in Greece with its 360 degree views over the countryside.
Corinth Area. https://www.flickr.com/photos/stanbr54/albums/72157711755443483

When you get to the road heading south to Nafplio instead turn right. About 5km will bring you to Ancient Nemia. It had sister games with Olympia and its stadium is still there. Its a great short stop.

There is lots to do around Nafplio which is a great place to make a base to visit the surrounding sites.
Nafplio https://www.flickr.com/photos/stanbr54/albums/72157632094108982
Images of Ancient Nemia are in this album.

On the way south to Monemvasia ( great choice be sure to spend a night in a period room within the village walls its a go back in time sort of experience) do consider a stop at Sparti to visit the last Byzantine city of Mystras. There is a small fortress and Byzantine cathedrals spread out down a mountainside.

Peloponnese, Mani and Monemvassia. https://www.flickr.com/photos/stanbr54/albums/72157711323535897

On the way to Pylos you might want to visit the charming village at Kardameli.

If your path takes you near Kalamata be sure to visit Ancient Messini. It is a huge site and may be the best ancient site in Greece.

Here are images of the area I have just suggested you visit.

Peloponnese, Mani and Monemvassia. https://www.flickr.com/photos/stanbr54/albums/72157711323535897
On your route to and around Pylos there are lots of Venetian era castles (fortresses) ,
Peloponnese Battle Castles https://www.flickr.com/photos/stanbr54/albums/72157645468134284

Have a great trip

I spent 13 days late September/early October of 2022 in the Peloponnese.

Thirteen days wasn't only scratching the surface of what's there.

The Peloponnese is filled with wonders, history, scenery, villages, locals and so much more.

I would recommend a good guide book and my favorite is the Cadogan Guide. While not recently published it's still relevant and with more info than any other book.

Bradt's good but not as much details.

You can check out my photos. Click on the first or any one to get a caption:

https://photos.app.goo.gl/2RwHoj4NAxBD7VcZA

We also found the Cadogan guide very informative.

We just completed 3+ weeks on rhe Peloponnese. Our favorites were in no particular order... Mystras, Messene, Dimintsana, and the deep Mani,based in Limini.
We especially loved hiking the gorge in Dimintsana and staying at the Amanities Guesthouse lovely ,helpful people who showed is the route and more.
We loved exploring from Limini outside of Areopoli, and staying at Vasilios Apartment Hotel.
Messene , was really nice and not many people. And Mystras was really interesting with wonderful views. We also went to Kardymili and enjoyed rhe setting but in March most restaurants were closed.
The Deep Mani was fascinating, exploring viliages and the rugged landscape.
We went other places as well and enjoyed everything . We too used both the Brandt and the Cardogan guides as recommended by the other posters here. Enjoy!