I met some friends this week that took me to Hannesarholt (address is Grundarstígur 10) and I couldn’t recommend it more! It was the home of the first Prime Minister, and now does revolving art exhibits. They have a cafe that is also very reasonably priced and the food was DELICIOUS. One of the staff took us around for a bit of a tour, and they have well equipped meeting spaces on offer as well.
As I understand, the Icelandic government has not chosen to help fund this home, and they’re in a bit of a spot. I would really, really encourage anyone visiting Reykjavik to visit, have some wonderful food, and support a great cause.