Since mid-May is still off season you will have more options at better prices with less tourists getting in your way.
I see Santorini again as a destination. Is there a particular reason you picked Santorini? It does offer spectacular scenary but also crowds even off-season, higher prices and more of a tourist-oriented island rather than a more traditional and laid back island. If you have your heart set on Santorini then a lot more research on your part will make it easier to experience the island, but still expect crowds.
Naxos is lovely, one of my favorite Greek Islands with an excellent combination of Old & New World Greece. You could spend days there and still not see it all. The ride from Naxos Town over the mountains to the small seaside village of Pollonas offers some of the most spectacular scenery anywhere with views and vistas of hillside villages, churches, cliffs, ravines, the ocean, rural areas, goats, sheep and will give you a feel for the Old Greece. The island is filled with centuries-old Byzantine Churches, lovely mountain villages of Chalki, Apiranthos and Filloti and lots more. I would spend my time there rather than Santorini.
Athens is Athens, wild, crazy, millions of people but one of the best bargains in Europe with World-Class archeological sites and museums, plus the Plaka, Central Markets, Anafiotika, Monistiraki Square, Psiri District and lots more. There are the usual tourists spots but Athens also offers many out-of-the-way areas tourists don't go to that still will give you a Greek Experience.
The Peloponnese would be perfect, however, it would help if you have experience in Greece. Nafplio is easy to get to and is one of Greece's loveliest towns and a short distance from Mycenea, Epidavrous and other ancient sites. It would be a good place to base yourself.
The rest of the Peloponnese would need to be explored with a rental car. It's a large area filled with wonderful villages, towns, cities, more archeological and historic sites, beaches, mountains and the Mani area would be another-worldly experience, but again, research is needed.
Lots of options for Greece other than the usual tourist-oriented islands and mainland but it means doing the leg-work to discover why Greece is one of the best bargains in Europe without spending a huge amount of money for the typical travel agent's version of Greece.