We saw this from the outside when we were on a walking tour of the city. I don't think you can go in but it does have a sign out front with information about it. Interesting piece of history in the overall scheme of historical things in Akureyri but not very exciting otherwise.
This oldest house of Akureyri can easily be admired from the street in front of it. A panel with information gives you all the details about its history. Have a look and move on, its nice, not thrilling