Naxos

You will not have enough time to fully explore all of Naxos in a week. There is lots to do and see, some antiquities in the interior, mountain villages with lovely hikes, Great beaches along the south coast and it will take you 2 days just to get the hang of Naxos old town which is a maze of back alleys going up to the Venetian era Kastro.
Here is what you can look forward to.
Around Naxos town 2022 https://www.flickr.com/photos/stanbr54/albums/72177720299959098
Back to Naxos 2022 https://www.flickr.com/photos/stanbr54/albums/72177720299940917

Trip around Naxos https://www.flickr.com/photos/stanbr54/albums/72157634605629689
Chalki and Vivlos villages https://www.flickr.com/photos/stanbr54/albums/72177720299950915

Naxos 2017 https://www.flickr.com/photos/stanbr54/albums/72157663620712358

We spent four nights on Naxos and felt like we needed at least one more. We did one hike (to top of Mt Zas) but there are many more we could have done. We originally chose Naxos for its beautiful beaches but ironically only spent a few hours swimming because we were so busy doing other things. We also felt a bit like we had “cheated” Naxos town as we were so busy running around seeing other things.

I have no doubt you can fill your week.

I agree. And your boys may enjoy Flisvos Sportsclub, at the far end of St George Beach (opposite of the town). There they can rent water sports equipment — windsurfers, jet skis, etc. It’s a great place to watch the sunset too.