Question for the group. We will have 4 nights in Naxos. We will have a car. We are staying 2 nights in Santorini, then taking a ferry for Naxos for 4 nights. Should I just explore Naxos for the time I have, or plan a day trip to another island. Thanks.
By only having 4 days in Naxos, you will not be able to see the whole island, but if you absolutely want to do a day trip you can contact a local agency such as Zastours which organizes day trips to the small Cyclades (Koufonisia).
That said, it would be a shame to lose a day of car rental by spending this time on a boat.
Since four nights means three full days, I would spend all of that time on Naxos. We spent four nights there and were not able to experience everything it has to offer. The island is large and you will have more than enough things to fill those days.
We were on Naxos for four nights. We had wished we had more time so I would certainly would not wanted to day trip to another island. It is a large diverse island.
Naxos is not a small island and 4 nights does not give you sufficient time to fully explore. Here is why you should spend every minute available to you on Naxos.
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
You really don't have enough time for another island, but ferry schedules permitting, you could possibly spend a day on nearby Paros.
https://www.ferryhopper.com/en