The recommendation for Crete is a good one - we didnt go there but most of the locals we chatted with are big fans of it and with that much time, its a great add on.
I mentioned in another reply to you about Naxos which was a 40 minute ferry from Santorini. We went to this island on the recommendation of the RS podcast and it was wonderful. The island is much larger than Santorini and Mykonys but maintains a boutique feel. It has all of the beaches, ports, sunsets (as good as Santorini) plus many more friendly locals, they are more invested in the lifestyle there rather than the tourist. It has everything you need and was so friendly and safe, not to mention a fraction of the expense. We stayed on the beach, with a good room, balcony and view for $80/ night. You will find many European tourist there - as they have all discovered this place too.
We ventured away from the Hora (main town) on a 4x4 quad bike (easy to ride and limitless access to all the sights) we rode the circumference of the island and discovered so much more than the beaches. Naxos is known for its cheese, agriculture and olive oil. In the town of Chalki (about 25 mins from town) there is an "walk" around the town that was mesmerizing. steps off the town center, you are greeted with a stone wall lined path that farmers have used for centuries. There you will walk through centuries old farmsteads long out of use as well as active farms, with sheep, darling goats with tinkling bells and active churches from the 1600s that you can walk right into. This walk is really how the country folks live and is like being transported back in time and was such a serendipitous find. As we were returning to town, a spry senior Greek fellow approached us and and was very interested in walking with us and telling us the history of some of the farm houses, how old they were (200 hundred years), showed me how to give a goat a fig treat (yeah) and to tell us about living there, he was charming and it was such a treat.
This island felt safe, welcoming and unspoiled. I highly recommend it.