If you have seen pictures of Iceland, you've probably seen pictures of one famous building: this church. It is definitely worth a visit.
If you are lucky, there will be someone playing the church organ. But if that's not the case, you can just walk around or go up the tower and have a great view over Reykjavík.
Entrance to the church is free of course, but entrance to the tower is 1200 isk (about 9 USD).
There is free parking around the church.