Plaka or Pyrgaki (Naxos)

In my opinion Plaka is the best beach in Naxos. It certainly is our favourite. It is at least two kilometers long and is serviced by a string of hotels and tavernas on the other side of the road with no buildings on the beach side which makes for great sea views. There is regular bus transportation into Naxos town so if you decide to have a drink you can still get back to Plaka. Of course Agia Anna and Ag Prokopous have villages so that provides some additional opportunities and a different feel.

There are two distinct areas of Plaka where there are dunes which hide the minimal bathing suit places so those areas can be avoided. Some toplessness might be experienced anywhere on Plaka.

Here are images of the beach and the hotels and the tavernas.
Plaka beach tavernas hotels https://www.flickr.com/photos/stanbr54/sets/72157655106193251

We (mom, dad, 3 tween/teens)

For kids that age, I'd choose the lodging closer to town. They will want to do some exploring on their own and not have to rely completely on mom or dad driving the car. The wish for seclusion comes at a later stage in life. :-)

Im also wondering about the "semi nude" beach area at Plaka, as my
kids might be taken aback (Im not, and don't care if the kids see
this)

To be quite honest... your kids would be the first teenage kids I hear of who are taken aback by seeing semi-nude people. Most kids that age are simply curious, in particular about these things. So if you don't have any issues with that, why should they?

We will be renting a car regardless to see the island, right?

The Naxos specialists will have to chime in on this (I've been to Naxos for day trips from neighboring islands only). We have been on many Greek islands and never rented a car except maybe for a day or two to get to some really remote spot. Most Greek islands have a very good and punctual bus system. Another reason for staying near town because that's going to be the hub.

Great. Things I hadn't considered. This helped me make a choice (and when there are 5 thousand to make, its a great help ;)

Jessica

Frankly, kids the age of yours want to be where other kids are.... they don't want a cozy isolated family experience. And Naxos is one of the places where it's safe for parents to let teens wander a bit ... very family-oriented. Ag. Prokopios is the closest outer beach, has busses to Naxos Town every 30 minutes, and does have a lot of families with kids the ages of yours... and a fine wide beach. The trick is, to get a place right ON the beach, not a hotel where you have to walk down a hot & busy road to get to the sands. The place I've sent a lot of families is http://lianahotel.com/ -- it faces directly on the water, has several buildings including apartments, plus a pool. But do not dither; it fills up MONTHS in advance.

Of course, for Teens, St. George Beach is fun tho crowded in July because it has a lot of water sports AND it's a 5-10 minute walk into town and the Waffle House, Ground Zero for Teen-gathering. Some serenity can be achieved by booking lodging on the far end of the beach, where things thin out.... the best place IMHO there would be Villa Naxia, with lovely decor, just yards off the beach, and family apartments. but again, no time to dither, VN also fills up months ahead. (NOTE: in Greece you can reserve risk-free because almost all places allow cancellation without penalty as near as 2-3 weeks ahead of date. So you could reserve in 3 beaches, then decide).

On a side note, THAT...

They will want to do some exploring on their own and not have to rely
completely on mom or dad driving the car.

... and THAT...

Naxos is one of the places where it's safe for parents to let teens
wander a bit

... is going to give YOU some seclusion. :-)

Thanks all. We got a place a short walk from Plaka :)

Now on to Crete ...