Hi Andrew ... As we say often on this forum, in september the BEST place to be is at St. George (Ag. Giorgios) beach, because you get a lovely beach view, it's quiet by night, but just a 10-15 minute walk to the attractions of cafes, tavernas, nightlife, museum, shopping etc etc. There's only one problem -- Noplace in Naxos will cost at much as $300 per night! That's the kind of problem we like, hey! In St. George, there really are only 3 upscale hotels -- all have pools, amenities, uniformed staff, that kind of thing. This
SKYMAP - http://www.skymap.gr/apps/site/viewmap/?mapid=29&cid=305 gives a pretty good birds-eye view of town & beach ( you can move the map around -- not complete on hotels of course because it only names hotels that pay for inclusion! But all 3 of these do.
• NISSAKI HOTEL, at he very closest end of beach, on "the Point" , is quickest walk to town. Very attractive and of course superhandy (see its website). The only reported drawbacks are (1) not many of rooms excpt top suites have a full sea view, (2) it has small "beachfront" but in fact, it's not a good place to go into the water... so you have to walk about 100 yards down the beach and (3) this is just my personal opinion; they put the pool in after they built the hotel, so it's kind of wedged between 2 wings, just a pool surrounded by cement, no landscaping (a bit motell-y for an upscale place) But it gets excellent reviews.
• NAXOS RESORT BEACH HOTEL is toward other end of beach, is back from sands about 100 yards but has grassy frontage in between & nice greenery around the pool.
• GALAXY HOTEL, mentioned above, is next to it, a bit back from beach, fronts on busy road but back of hotel is toward beach.
If you wish to visit other beaches, a bus goes hourly in September, takes from 20 minutes (Ag. Prokopios) to 30 minutes (Plaka). The main bus Starting point is by the ferry pier... but if you stay at Galaxy or Naxos Resort Beach, you can pick the bus up just a block or so away (I believe it stops on the corner across from the Police station; your hotel will know).