We had a great stay at Tree Garden by the beach. The studio is beautifully decorated and spotlessly clean. It's five minutes walk from the beach, and really good restaurants and tavernas. The roof terrace is a great spot for catching the sun or star gazing at night.
Kantouni is a great base for exploring Kalymnos. We hired a bike from Stefanos up the road which was a really good way to get around. There are fantastic walks nearby. We walked to the monastery on the hill above the local beach and around the headland to St Photis church - both easy, close by and highly recommended. We also walked the Italian path from Pothia to Vathy which was spectacular (although we got a bit lost at the end).
Kalliopi and family were great hosts. Jack picked us up and dropped us off at the port. He also showed us local sights, bought us water when we arrived and even gave us some fruit from the family's trees t take home. Altogether we'd definitely recommend staying here.