About the location
Although the first people already came in 870 to Iceland, the area was growing very slowly and the city itself was founded nearly 1000 years later in 1786. The city has some nice architectural highlights for photography like the Hallgrimskirkja, a church that looks different than any other church you might know, or Harpa, which is a pretty modern concert hall.
Besides the already mentioned photo spots in the center of Reykjavik, the city is a good starting point for the first night(s) because the "Golden Circle" (Öxararfoss waterfall as part of Þingvellir, Gullfoss waterfall & Strokkur Geysir) isn't that far away and can easily be done within one day (you need about 4-5 hours for 300km, so plan with at least 8-10 hours if you want to see them all).
Overall I wouldn't recommend planning too much time for a stay in Reykjavik. It's a really nice city, but let's be honest... if you are a photographer you are usually not coming to the beautiful country of Iceland because of the architecture, but because you want to see the amazing landscapes and waterfalls.