To get to the island of Grímsey you can take the plane, or you can take the ferry.

The ferry takes about 3 hours one way. You could go back and forth in one day, but you will only have about 2 hours on the island if you do. Which is enough to see a lot of puffins (if you go between May and half August), but I personally just love spending a night there and enjoy the island a little longer.