In reply to pyrrho101:
Hi Pyrrho,
Just returned from my 3rd visit this morning!
Cannot recommend Hotel Philoxenia highly enough.
It is located at the foot of Grande Grotta, so location could not be more perfect. Cuts out the need for a scooter, as so many crags are walkable from there.
Nikolas (owner) was born and raised in the hotel, so knows everything about the island and the area and can sort out any problems for you. He is also unusually high-tech for a Greek, so has access to web info other proprietors may not.
Views are spectacular both sides and the hotel is clean and cool and has 24 hour hot water (which is actually unusual on Kalymnos).
Only downside is that Wi-Fi is only available in the lobby/bar area, but not in the rooms.
http://www.philoxenia-kalymnos.com/#!/pageHome
Also - Neil Gresham has been staying there every year for the last ten years, so that says a lot!!