I live here on a Greek island year round and I've been to many, but I get lazy and I always plan to see more "next year". I've always fancied going really off the beaten track - either Kestellorizo, Karpathos, Kasos or Kythira are all served by OA.
The first three - I think are served on the Dash 8 from Rhodes, rather than directly from Athens. I think the flight goes Rhodes-Karthapos-Kasos so you can still "Island Hop" in the true sense of the word. I think it's a 15 minute flight between the two islands. Kastellorizo is very remote and also right off the coast of Turkey (but I don't know if there are day trips) and a lot closer to Cyprus than Athens.
I've never been to any of these places but I'm sure they're all nice.
Or, try Skopelos or Alonysos. You would fly to Skiathos which is nice, but VERY crowded and over-touristed in the high season. Then it's only a short ferry ride to the quieter islands.