Another tip about bus travel in Naxos, without a car. The bus service is very good & regular, but outside of high summer, its schedules are oriented to local needs ... so are in the morning (8:30 - 9??) for townspeaple going out to work in villages, and village people coming in to the port to work. Then same deal in late afdternoon. In between there might be just ONE bus run ... about time kids get out of school.. So, you cant just zip out & back whenever u llike.... but there's an added option:
Get the cards/mobile numbers of a couple of taxi drivers in th port town -- your landlord probably has 2 uncles in the business. . Then u could use a taxi 1-way ... for perhaps about $10? Ask in advance. THen, for example, you could take the morning bus up to Apiranthos & vicinity, then if you were ready to come back to the beach area by noonish, and there was no scheduled bus unitl 3:30, you could use your phone to get a taxi. We actually did this when 3 of us were out scouting a ruin on a hillside, andhad planned to bus back to port, but stood in the wrong place & saw the bus zoom by ... but we had a phone & a card, so were OK.
The variation would be to taxi upto a village, allowing time to visit & catch a late-dy bus back to port.