Help! recommendations for Greek holiday please

Hydra is beautiful, picture perfect and motorised traffic-free.
Paxos, Paros and Naxos, all worth visiting and not far from Athens by ferry or Flying Dolphin.

Sorry I misread. You have been there.

Santorini. Fabulous.

Lesbos-Authentically Greek..
No mass tourism,traditional tavernas,beautiful beaches and green forests. Also fascinating history.
Having visited many Greek Islands, Lesbos is the only one we have returned to.

Rhodes is interesting - lots to see. Go to Rhodes town for 3 nights find a boutique hotel. Then head for Lindos- it’s a world hertitage area so they haven’t been able to ruin it.
Parts of Corfu still lovely. We stayed at Barbati last year - long strip of shingle beach and enough nice tavernas to enjoy in a week. Not a village feel though as a road runs through it! Kassiopi popular too- several bays, harbour, lots of tavernas. Very pretty by the sea. Cephalonia- beautiful. Assos or Fiskado- authentic Greek but hilly & a journey from the airport

Went to Santorini, Paros, Naxos and Mykonos last year. Naxos was by far my favourite. It’s an up and coming island and not quite so touristy- beautiful old town and coastal walks, a castle and some lovely bars and restaurants along the front. Very pretty.

Rhodes is my favourite, I love Rhodes town, the history is fascinating, there’s loads to see.

Lefkada is lovely, so is Skiathos and you can get a ferry to Skopolos . Unfortunately most of the main big islands are busy and touristy . For more authentic an island requiring a ferry might be better . Friends recommended Paxos , you get the ferry from Corfu .

Recommendations? Don't until you can be sure the heatwave is over.

Remember to take account of the temperatures.

My friend love Kithera (not sure of spelling). It is authentic but not sure how many tavernas!

Sorry OP I have just reread your post and seen that you have been to Santorini 🤦‍♀️

My favourite Island is Skiathos, on the mainland Parga is gorgeous.

Be very very careful. A big travel company, part of the FTI group, has just gone bust. Our DS and family were going to Greece, but now they have been cancelled and need to look for an alternative.

Santorini, beautiful.