~5 day trip to Greece - solo - Athens? Naxos?

Flying in from UK so not too far.

I want to book something last minute for around 5 days in the end of september. From what I have gathered Naxos seems ideal for me - less touristy/great scenery/beach/chilled

As I only aim to spend 5-7 days, should I fly directly in to Naxos, or perhaps split the trip into Athens and Naxos?

Id rather enjoy the time in a few places then rush place to place.

Given flights are accomodation is relatively cheap from UK, it also doesnt seem to make sense paying expensive transportation fees e.g. ferry to ferry e.t.c, which is leading me to perhaps just do Naxos and then do daytrip elsewhere?