Hi, we've been to Greece 2 times already, and have seen: Paros, Santorini, Mykonos the first time; Kos, Kalymnos, Nisiros the second time. I have to say, I absolutely LOVED Kalymnos, not least because I do a bit of rock climbing. We just got on our scooters and rode everywhere, found secluded beautiful bays, etc. The island was JUST BIG ENOUGH to keep us busy for a few days, but small enough as to not be overwhelming. The traffic was pretty low-scale, which was very important to us. The number of tourists was OK, in the sense that there were enough many people to keep some nice restaurants and bars open, but not as many as to render the place a tourist trap.
Kos on the other hand, we found pretty awful to be honest - noisy, touristy, heavy traffic. Not authentic at all.
Would Karpatos be similar to Kalymnos? Any other islands that we should consider? Not tiny-tiny ones, but similar in size to Kalymnos. Ideally, in Dodecadenese or Cyclades, but not necessarily.