In between Naxos and Amorgos lie six smaller islands. All but one of them off of the southern tip of Naxos, with good small ferry connections to them from the larger two islands six days a week in summer.
Donoussa, the largest of the six, lies off of the eastern coast of Naxos, and has a good number of sandy beaches, places to camp out, good walking, a couple of villages, and a nice enough port with rooms, though one should book ahead in August.
Of the others, the most populated is Ano Koufonissi, with fine beaches, plentiful accommodation, a campsite, good tavernas, a campsite, and with all this, lots of tourists in season. Kato Koufonissi , though mainly inhabited by goats, has some quiet beaches, a taverna, a 15th of August festival, and kaikia (caiques) that go to it.
Less striking than Ano Koufonissi, though more Greek and less touristic, is Skinoussa, with plenty of beaches and trails, as well as eating and drinking places. The farthest island from Naxos where people live is Iraklia, which also has a 15th of August festival and another near a large cave on the 18th of August. Sandy beaches and camping places are among its other offerings.
Keros island is an archaeological site, reachable for a price for the aficienado. These smaller islands can offer some respite from the crowds that visit Naxos and Paros in summer. Click map for more info.