Ferries between Naxos and Milos don’t start until June 7th (one each way, every day after that). Ferries between Santorini and Milos start April 28th and there is one every day in each direction. And there are always ferries between Naxos and Santorini. So if the dates work I would fly to Santorini (the longest leg) then ferry to Milos then Naxos and back to Athens. But if you need to travel between Naxos and Milos before the 7th then ferry Athens to Milos to Santorini to Naxos and back to Athens.
The almighty church has kept nightlife in check. If you must see and be seen, head to quietly glamorous Astivi or Stoa bar, on miniature Agia Lesvias square, in Hora. Beach life is generally languid and low-key; Psili Ammos and Livadi Geranou are our favourite hideouts. Dinner reservations are essential at Benetos, for Med-Asian fusion on an organic farm, and Lambi for grilled fish on a purple pebble beach.