Here is my list of the most popular places for a photo shoot in Iceland:
Places not far from Reykjavik:
You can take beautiful photographs in Reykjavik itself, walk on the water and through the volcanic landscapes with moss in the suburbs, or go towards Kleifarvatn. Without leaving the airport at all, you can shoot in the Blue Lagoon or near it.
Also a cool place near Reykjavik and Keflavik is the active volcano Fagradalsfjall. It's not a short walk, but absolutely worth it! By the way, you can also have a ceremony there.
Trip for one or more days, the most popular options are the South coast near Vik and the Snaefellsjokull peninsula. The most popular and easily accessible sights are located on the coast of Vik:
the black beach with columns of Reynisfjara, the lighthouse of Dyrholaey with magnificent lakes, the waterfalls of Skogafoss, Kvernunfoss and Seljanafoss (Iceland's most Instagrammable waterfalls!), the banks and the Fjadrargljufur canyon. Regarding the popular Geyser and Gullfoss: they are smaller sites for a photo shoot, but they are definitely worth a look during the trip.
A little further from Reykjavik, behind Vik, next to the Jökulsárlón lagoon and Diamond Beach, views of the Vatnajökul glacier and the Svartifoss waterfall, but it is better to plan for two or three days of shooting. By the way, in winter, in this case, ice caves develop and are protected.