When we landed, we were told that "so many people" were coming today that at least one extra flight was arriving today as well, and that we should be at the airport by 1:30 p.m. (Our flight departed at 2:15 p.m.) It's a very short flight from Akuryeri to Grimsey, about half an hour. The cockpit was open - there wasn't even a curtain - and no security to speak of at the airport, nor much on the plane ("Wear your seatbelts, turn off your electronics, and have a good flight!").
It's a small island, about two square miles, and easy enough to walk from one end of the island to the other; there are hiking trails all over the place. We didn't go from one tip to the other, but did walk most of its length several times.
It's beautiful; lots of open fields and rocks that lead right up to the ocean.
We walked from the guesthouse closest to the airport to Miðgarðakirkja, the formerly Catholic church that's now Lutheran. Small though it was, an early Icelandic Catholic bishop had consecrated the church, dedicated to St. Olaf, patron saint of Norway, in the 11th century, which the understanding that there should always be two priests at the church who would sing Mass daily, but twice a day on special occasions.