Hallgrímskirkja Church is one of the most iconic places you will see when you visit Reykjavík. It is located in the city center, upon a hill so you will see it wherever you are in the center. It is a lovely church with great architecture and amazing views from the church tower.
The Church Tower is open to the public during the day (for opening hours please see http://en.hallgrimskirkja.is/information/the-tower/ ) Hallgrímskirkja is the largest church in Iceland and the tower is 73 m high. It provides a 360°panoramic view over the city. The church is also famous for its amazing pipe organ that is worth seeing.
The Church is located in the city center of Reykjavík and therefore close to many interesting sites. In front of the church you will find a statue of Leifur heppni (Leif Erikson) who discovered North America.