I showed up in Gudhjem without reservations. I found that most of the places in town were either booked with school groups or didn't have owners around if they weren't expecting anyone to stop by. I passed Pension Koch from the bus stop on my way to the harbor, and stopped by to see if there were rooms available. The cleaning staff called the owner and was able to give me a room (the cleaning staff at other places I stopped by did not offer to do this).
I had a first floor room in the main building. It was cosy and quiet. The breakfasts were amazing. Bicycle rentals are available. It is right across the street from a main bus stop, so, for someone without a car, it was very convenient. The walk to the harbor was under ten minutes, downhill. There were also two grocery stores nearby, and a bank with an ATM machine.
In the evenings, I enjoyed sitting outside, looking out over the ocean. I often sat in the parlor at night to read when it got too dark to sit... More