It's our 1st time as well and I know what you mean. It's always nice to take in a new island.
Last year, we had a taxi transfer,(decided we'd push the boat out as it was our 25th anniversary), great on the way to the hotel but on the way back it came a lot later than the coach and I was really worried that we were going to be left behind. We had no idea who to contact as it had been arranged by Thomsons and the hotel couldn't help. They just kept saying don't worry! We got there a lot later than the coach and had to wait outside in the hot Kos sun. It would be different in Agios Stefanos though as the transfers could be arranged with the local travel agencies.