Living in Greece, I've stayed in many accommodations, cheap and not so cheap, and Agnanti is probably one of my favourites. The rooms are wonderful, with kitchen facilities, table and balcony. Comfortable beds, and great bathroom - it was really tasteful.
The breakfast on the terrace was taken together giving you a chance to catch up with other guests. The highlight is the sun terrace by the sea. There are no sandy beaches in Kastelorizo (not that I found) but this foot has perfect water, kayaks to paddle around on. Great location.
Ok so wifi wasn't great in the room, but for once I didn't care. It was a good to get away from it. Worked great elsewhere even by the water
Mr Vassilis will meet you from the port, help you with your arrangements. I really liked this place and I hope you will too