Becky, plan your flight logistics before you book your hotels (and BTW, in hotels don't go for the rock-bottom nonrefundable rate; the risk is not worth the minor savings). You might also consider flipping your sequence depending upon WHEN your flight from US arrives in ATH. this is a price/time decision; here's the deal.
Only 3 nonstops (priciest) from N. America -- from PHL, JFK or Montreal -- arrive between 9 - 10:30 AM, giving you the most choices of onward flights.... If you opt for cheaper fare, you change in Europe and may not arrive until 2-5 pm NAXOS only has 3 flights per day, small modern turboprops, 40 psgrs, so unless you arrive by 10-10:30 you can't get their noonish flight and have a dreary airport wait. SANTORINI, on other hand, has many flights per day, on into the evening... so if you have a 1-stop or 2-stop in Europe, you still could get there by sunset. I'm guessing that, since you're not kids anymore, you might bite the bullet & go nonstop ... especially if you don't live on the East coast & thus have a flight-leg just to reach PHL-JFK-Montreal.
If you plan to fly into ATH & change for an island Start checking island flight schedules in late 2019, on Aegean & Sky Express. Aegean "newsletter" -- https://en.aegeanair.com/newsletter/?a_id=2183&related=1&session=BHtOo7mo -- alerts you to "sale" prices early in year.
As for your interests, Naxos is ideal; In late may I alway stay in St. George beach directly adjacent to Naxos Town.... easy stroll to all the attractions of town -- cafes, museums, shops, etc -- and local bus takes you to a row of other fab beaches, or to mountain villages. Great cuisine, dramatic inland landscapes, farms, ruins, history. Aaah. Go on booking.com to check it out; look at "map view" for accommodations directlyon the sand. You'll do best with 2 units, either a studio w. seaview balcony & ktichenette, or a 1-BR with main room/balcony/kitchenette. There are at least 7-8 theat are diectly on sands, or a few yards off, and if you research & reserve early, you'll get lovely units. Just a few: Studios Kalergis, Studios Thomais, Villa Naxia, Hotel Kymata, Hotel Palatia, Hotel Ippokampus, just a start. Enjoy your homework & planning - the more research, the better the experience!