avoid the mass toerism in Greece: hiking, snorkeling, ..

We hiked to summit of mt zas on Naxos which is the highest point in the Cyclades. Not very crowded. There is a lot of hiking you can do on Naxos if you are interested in going to one of the islands.

The challenge is things are not that well marked. At one point I stopped to take pictures of mountain goats and my party went ahead without me. I crossed where I was supposed to turn and could not figure out where I was. Then I heard some voices and called towards them. The hikers waited for me and sent me in the right direction. So in my opinion, a few people on the trail can be very helpful!

You may want to consider the Peloponnese Peninsula. It has everything you are looking for and a rental car will be the best way to experience it.

https://www.greecetravel.com/peloponnesos/

https://www.greeka.com/peloponnese/

Lots of islands to consider also but if you want to island hop that means packing up and moving each time which takes away from your "fun" time.

https://www.greecetravel.com/greek-islands/

While staying in Nafplio we took the 'Sunken City' kayak trip with Pan Expeditions https://www.panexpeditions.com/ The water is beautiful shades of blue and turquoise. This tour includes a snorkel over remains of an ancient city/village and another snorkel over an underwater cliff. They provide all equipment. This particular tour spends more time kayaking than snorkeling, and there is a picnic lunch on a small, secluded beach. We saw no one else on the water or beach that day, this was in mid-June. After the paddle we visited Epidaurus on our way back to Nafplio. It was late afternoon and the site was sparsely visited. Pan has several active tours in the Nafplio area (Peloponnese).

We also took a sail from Chania that included snorkel time. My impression is that snorkeling is often included as part of small group boat-related activities in Greece.

+1 for Naxos and hiking Mt. Zas

Naxos fits your description - was just there. Phenominal windsurfing at Mikri Vigla. We snorkeled the back (south) side of this area where the rocks blocked the wind - it was just incredibly beautiful. Loved it.
https://www.greeka.com/cyclades/naxos/sports/windsurfing/

Hiking is beautiful on almost all islands I have been to so far. Skopelos if you like forests, Naxos or Paros for Cyclades charm, Santorini for the spectacular views (and the crowds), and tons of lesser-known islands. Many islands have ancient donkey paths that nowadays make great hiking paths. I agree that they are not always well marked though.

but the paths not too crowded?

The Greek are supposed to have a saying: "Only donkeys, women and tourists walk on foot." :-)

Anyway, most tourists don't really do much walking either except to the beach. So once you move away from the roads just a little bit, you'll be by yourselves.

We would also like to visit the coast

Just be aware that that's where everyone is. If you want to avoid crowds, go inland.

hike to some lesser known archeological sites.

Many islands have lesser known archeological sites that you can hike to. Just be aware that these lesser known sites usually are lesser known for a reason. There may not be all that much to be seen.

Lovely new ideas -- but this request was posted in mid-April for a trip in june... OP is long since back home.