Among the twenty or so Cyclades islands there are a few which are relatively less invaded in summer.
Kythnos (1 ferry 3 times a week, 3 hours crossing time)
https://www.visitgreece.gr/islands/cyclades/kythnos/
Serifos (3 to 4 ferries per day, 2 to 4 hours crossing time)
https://www.visitgreece.gr/islands/cyclades/serifos/
Kimolos (3 direct ferries per week, 4 to 5 hours crossing time or reachable every day via Milos with 5 ferries per day Piraeus→Milos)
https://www.visitgreece.gr/islands/cyclades/kimolos/
Folegandros (1 to 2 ferries per day, 4 hours crossing time)
https://www.visitgreece.gr/islands/cyclades/folegandros/
Amorgos (1 ferry per day, 7 hours crossing time)
https://www.visitgreece.gr/islands/cyclades/amorgos/
Tinos (7 to 8 ferries per day, 2 to 4 hours crossing time from Rafina port)
https://www.visitgreece.gr/islands/cyclades/tinos/
Sifnos (3 to 4 ferries per day, 3 to 5 hours crossing time)
https://www.visitgreece.gr/islands/cyclades/sifnos/
Looking for less busy and popular and easy to reach is not without compensation. None of these islands have an airport, so you will have to take a ferry.
Outside the Cyclades there are also for example Kythira and Limnos which have an airport with direct flights from Athens
Kythira (Ionian Islands)
https://www.visitgreece.gr/islands/ionian-islands/kythera/
Limnos (or Lemnos) North Aegean Sea
https://www.visitgreece.gr/islands/north-aegean-islands/limnos/