Went there a couple of years ago, really enjoyed it. 4 nights is perfect in Naxos. Spent 2 days in Athens before to see the major sites there, happy we did.
We flew from Athens, if you book far in advance the price of flights or ferry were about the same, and from the main hotel parts of Athens it's about the same amount of time to the airport or the port. Athens airport security was reasonable so no need to get there more than say 75 minutes before departure. Naxos Airport is TINY and most people arrive 30-40 minutes before departure. One thing to note is that there aren't any taxis usually waiting at Naxos Airport to pick up anyone, they are reserved, so make sure you have your hotel or rental help you reserve a taxi to pick you up, it's around 25 euros to the main places within a 15 minute drive or so (same on return).
We stayed at Agios Prokopios beach and really enjoyed it, the beach is great, there are plenty of places to eat there, but it's not like a late night party area generally. Also only 20-25 minutes bus ride into the main town, and 10 minute taxi ride from the airport. You can also rent a car there for a day or two if you want to drive to some of the inland sites/ruins, which seemed to be a popular choice. If you do end up staying in AG, eat one dinner at Giannoulis, it's super popular because the food is good and the vibes are immaculate. Line is constant but we got there early (hungry kids) around 6 PM so barely waited.