Háteigskirkja, located on the rise just to the east of Reykjavík's ubiquitous Hallgrimskirkja (just above Kjarvalstaður museum, number 29 on this map.) It's certainly a very lovely building, built in the Moorish style as the church web site notes, and probably as close as Iceland gets to a fantasy castle.
One thing that I find a little amusing is Icelanders' fascination with their illustrious history. Though I respect that our people have quite a collective story to tell (vikings, sagas, forays to America, volcanic destruction, etc.) there's little here structurally to show for it all.
What I mean is that there are only a handful of buildings that pass the two century mark, and ultimately the "Icelander" as a phenomenon is just a bit over a millenia old. When I went to Norwich, England, last February and drank a draft (or two!) in a pub, The Adam and Eve, that has been serving continuously for 750 years I finally really understood what old meant (and that's aside from Bill the Conqueror's castle, erected a couple of centuries earlier!) Californians have pretty much the same problem in that there's barely a thing that's older than a century and a half, aside from an adobe mission or two.
I guess I'm just a sucker for the really old, for history, for structure. Passing by this church the other day with the waxing moon between its spires, I guess I kind of wished it really were an ancient and storied castle.