When my father and stepmother went a number of years ago they stayed mostly in rural boarding schools that I guess open themselves up for tourists during the summer when school is out. I remember he said it was mostly "Elder Hostel" kinds of groups staying in them, but a very reasonable way to see a lot of different parts of the country. They weren't part of any group and I don't think they had trouble booking beds.
He also said that he looked forward to taking cabs because all the drivers were female and hot.
Besides the above-mentioned Heima, two other films that may make you want to visit Iceland are
Cold Fever and
No Such Thing. I'm particularly fond of Cold Fever.