Rachel -- We are about your age, and we were also debating between the Kymata and Kalergis for our visit to Naxos in May 2016. We chose the Kalergis and had a wonderful stay.
On our travels we almost always book balconies, for the view. But here, because the hotel is right on the beach, we chose one of the ground-floor patio rooms. How often do you have the opportunity to walk a few steps from your room to the sand?? We still had a beach view, from our patio. The patios aren't totally private from each other; they are separated by low walls. But the hotel is set back from the beach, behind a low wall, and patios are screened from the beach by plantings. So you have privacy from people walking by.
At the Kalergis, you don't get a wonderful breakfast like at the Kymata. But you do have a little kitchenette with refrigerator and stove. So we stocked up on fruit & yogurt from one of the many nearby markets. And a couple of times we got wonderful fresh croissants from a bakery up the street. And then we'd have a lovely, quiet breakfast on our patio.
In mid-May the beach was very quiet. Very few people. No noise at all. Next door to the Kalergis is a restaurant/beach bar with sunbeds and umbrellas available for customers (including hotel guests) at no charge (at least when we were there). It was wonderful to relax there after a long day of sightseeing.
Wherever you stay, I highly recommend walking down the beach (away from town) to Flisvos Sportscenter for happy hour. We walked by it every morning and saw jet skis & windsurfers lined up to rent along the water. But on our last evening, we walked up to its hotel and found it had a lovely "front porch" with couches and comfy chairs facing the sea. We settled in with our ouzos for a spectacular sunset and wished we had found it sooner!
I hope you have a wonderful visit to Naxos.