Hallgrimskirkje is visible from most of Reykjavik and serves as a navigational landmark for visitors. The massive basalt structure is currently being restored and the tower is completely covered by scaffolding. The soaring interior, however, is well worth a visit.

In clear weather, the view from the top of the tower is splendid, though windy. There is a fee payable in the small gift shop for accessing the tower. Take caution about how many go into the elevator at once. The sign says eight people at a time...this means eight small people. I'd suggest limiting the load to four American passengers. I personally got stuck in this elevator for a half hour when it was overloaded.

The organ is the largest in Iceland and on occasion, visitors get to hear it being played while on a visit. The statue in the square outside represents Leif Eiriksson, a gift from the United States on the occasion of the 1000th anniversary of the founding of the Althingi in 1930.

I thought it was kind of pricey, considering we stretched our time up there to maybe 10 minutes. Scaffolding was up on three sides, fourth side was completely boarded up, so I don't know what we might have seen otherwise. I did not think the scaffolding got in the way much (obviously the people charging didn't either, since you still pay full price), there are small windows through which to look, and the scaffolding bars were not in front of them. We were up on a beautiful day, but I thought the view from the harbor was lovely and this was just boring.

Totally under construction and covered with scaffolding.
Hope they get this over with soon.

I went up the church tower in early February, but the view was not the slightest bit impressive - if taking photos you have to zoom out in order to cut out any scaffolding poles and the view is very limited. The Perlan is much more advisable for views of the city.