If you visit the island of Naxos, you will notice that you will have different beach options.
If you plan of staying in Naxos town, you will have some beach option. At the feet of the Portara Hill, on one side, people were swimming but it was less tempting. We opted for the Agios Georgios beach. Still within walking distance from the town. Long sandy beach with eating options, it is a nice family place. It did not fell too crowded and if you which you can rent chairs under umbrellas.
If you wish to explore further away, some beaches are accessible via buses. Coach bus can take you to other region for you to explore or you can rent a car. If you are unfamiliar with the island, it is possible to loose time. The indication is so so but when you reach beaches like Agia Anna or Plaka it is very pleasant.
Sandy beach crystal water warm sun, beautiful day.
Some beach offers windsurfers and kitesurfers excellent conditions.
Agia Anna in addition to having a nice beach, it offers a variety of restaurants, taverns, cafes, bars,… Hotels next to the beach is also an option if you wish to stay there. The atmosphere is agreeable.
I wish we would had more time to explore more beaches but unfortunately, the car rental agency restricted our journey and visit of the island.