Several years ago, our ship spent far more time in Akureyri than was intended -- a one-day port call.  And for that day, a bunch of us on our Roll Call had booked what turned out to be an excellent private tour well outside the city -- one of the classic Lake Myvatn tours (Godafoss Waterfall, bubbling mud pots, Lake Myvatn Nature Baths, and more).  I highly recommend doing something like that in Akureyri.   However, because of weather that kept us out of another port, we docked in Akur