Naxos...how many days? plus a cruise

I was on Naxos for 4 nights from Oct. 16, 2019. I had hoped to take a day cruise to Delos for the archaeological site but it was 2 weeks past the end of the season. I stayed in a 2nd floor flat with a small balcony overlooking St. George beach where I watched sunsets with a glass of wine. There were a couple of restaurants within 10 minutes' walk and a well stocked grocery store and a coin-op laundromat. I took one full day bus tour that was interesting. There wasn't much to see or do in town. This was the tail end of the tourist season. My landlady said I was her last guest, the rest of the rooms were empty. In other words there's not a lot to marinate in. I spent my time just relaxing. I'm not a beach person either, but I did take a bus to nearby Agios Prokopios beach for a day, lounged on a beach chair with a sunshade, had a little wine and snacks and read a book.

Before Naxos I spent a week on Crete and a few nights on Santorini. Crete is probably much more suitable. I spent 5 nights in Chania, then 2 in Heraklion for the archaeology museum and a visit to Knossos. There are a few other sights. I absolutely adored Chania, lots of history, tons of good restaurants, fun shops to explore. If you rent a car, I believe the island has a lot of natural beauty as well.

I stayed on Naxos for 9 days in St. George Beach. This was the first half of October. Naxos Town is a short walk away or if you don't feel like walking there is a small town square with shops, markets and tavernas in St. George.

I did day trips via the bus to most of the villages, did a day cruise to Delos/Mykonos with Delos far more to my liking (history buff!)

There are other nearby islands you could possibly do day trips to.

October is off season but most everything was open, especially St. George & Naxos Town. It was pleasantly busy but not overcrowded like High Season.

Spectacular mountain road through the interior of the island, beaches, archeological/historic sites, many Byzantine churches, great food and just a wonderful island with something for everyone.

I stayed busy during my 9 days and never ran out of things to do, see or experience.

Bear in mind I was last on Naxos in 2013 so not sure if the tourists have decided Santorini/Mykonos is just to expensive and crowded and seek out an alternative like Naxos.

Peloponnese is a special place filled with wonders and it's history goes back thousands of years. Highly recommend it but it would take weeks to fully explore.

Can't go wrong with either Naxos or the Peloponnese but the Peloponnese is better experienced by renting a car.

As for Athens I always stay 2-3 days every time I go to Greece. There's more to Athens than the tourist sites/sights. It's better experienced by walking.

You can easily spend a week on Naxos and not see all of the island. We have been there 10 times with each stay a minimum of a week. We keep finding new things to see and do. On our last trip we found a new tour company that took us to places we never saw before. We took a wine and cheese tour to a remote farmhouse where we fed the goats, made cheese and had a Greek style meal. Then we went to a winery for a tour and tasting. Pick up at noon drop off at 9 in the evening.
If you visit the village of Chalki there are kilometres of good flat hiking trails in and around the village. If you still love a good hike /walk Naxos will provide the opportunity.

I think tommyk5 gave you a really good description of what Naxos is like.
Here is Naxos
Naxos town https://www.flickr.com/photos/stanbr54/albums/72157632094558042
Trip around Naxos https://www.flickr.com/photos/stanbr54/albums/72157634605629689

Naxos 2019 https://www.flickr.com/photos/stanbr54/albums/72157711294807761