Visit Reykjavik just dug up this old film somewhere on the net which was shot by tourists in Reykjavik in 1926. It shows what the capital looked like and though it's been 86 years, most of these houses are still there, we still have the same three men as the entire police force and some of those kids do look familiar. Maybe I know their great grand children... Heck, maybe I am their great grand child ;)
In the beginning of the film you can see as they sail ashore. Make notice that this is at midnight! The big building there is now Radisson Blu 1919 though it is a bit further from the harbour today, as a landfill was created some decades back. You sometimes see crowds gathering in the spot where the crowd is starting at 0:39, but nowadays they're in line waiting for a hot dog at Bæjarins Bestu.
Most of the shots are taken at the corner of Austurstræti and Pósthússtræti standing outside Landsbankinn, which still stands and is still the same bank. Well, same name at least ;) The church is the Domkirkjan (cathedral) by Austurvollur.
If you're an Icelander watching this, show it to the eldest in your family and see if you can recognize some of the faces :)
Do you see anything you recognize from your visits to Reykjavik?