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I was there about 8 days, and we had help from local guides.
As far as my favorite places:
1 - The Glacial Lagoon in Jökulsárlón - its truly stunning. The lagoon side is a study of symmetry and reflection (#4) but I was bored with it after a while. It is never the same however, as the bergs change and move, and the setting sun can provide a dramatic backdrop. The ocean side of the lagoon, where the bergs enter the ocean, is crazy. Beached bergs litter the shore during low tide, to be swept away later. Depending on when you come its either empty of full of them. Common photos are of the beached ice over some nice sunset or sunrise, but a pure gray morning offered something special here (#1). It is sadly a 4hr drive from Reyk.
2. The Laddrangur is very dramatic (#2), and was my second favorite place. I used the Big Stopper, but i am sure its not necessary. It would have been nice to have a sunset over the basalt stacks in the distance. There is also a tiny lighthouse there, but you need a good zoom to see it.
3. The Great Geysir (#3). For several reasons - its fun to try and catch the bubble, and it occurs frequently enough (every 5 min or so) that you are sure to get a great shot there.
4. Seljalandsfoss waterfall. Its pretty famous and over-photographed, but its worth a trip. Shooting behind the waterfall at sunset is extremely challenging as water is swirling in the cave and avoiding water droplets on the lens is hard. I'll post the photo as part of second set.
5. Öxarárfoss waterfall at the Ŝingvellir National Park is also a great Big Stopper moment. Plenty of rocks, etc.
6. Immense twin waterfalls, Gullfoss. A lot of different compositions can be had, from grand panos to individual streams and rocks.
The rest is just driving around the country. Icelandic horses are fun to photograph, they essentially pose for you if you get close. The moss covered lava fields are difficult - they're vast, and there is little for eye to grab on to. Little red churches with attached cemeteries are nice, and come out as good contrast with blue sky, green grass, red/white church - all primary colors. The Aurora is pretty hard to get unless weather cooperates. We were lucky to see it once.
2 and 4 are my favorite, especially 4, wow! How long were you there for? Could you provide a brief itinerary of your stops a favorite places?