If you are planning to come to Iceland for the first time, or if you just arrived here, I'm sure that one of the first places that you are going to see is the "Golden Circle".
There are tens of companies that offer day tours to what has become a tour that practically every tourist has taken. I will not dwell into how much of a circle or how golden it is, but I guess if it's your first time here, visiting Geysir or Gullfoss seems like a "must". Besides, it's conveniently situated for those who wish to do a round trip around the island.
However, one of the biggest mistakes people do is go on this tour and then come straight back to Reykjavik. What I'm saying is that there are other places, just as close to Reykjavik and just as amazing, but have not been massively advertised so at times go unnoticed. Just north of Reykjavik, you have Glymur, the second highest waterfall in Iceland, and its surrounding area.
Just south of Reykjavík you have an area called Reykjanes peninsula. If you came to Iceland on a plane, I can assure that you have already been there, as Keflavik airport is situated there. So is the Blue lagoon. I have to be honest here though, I do not like crowded places and I would rather go to a Vesturbæjarlaug swimming pool in Reykjavík or find a remote natural spring to dip in to. Plus, you get to keep a good chunk of your money by skipping that place.
Reykjanes is so much more than just those two places and I would like to suggest a small tip for those who wish to explore the area little deeper. Let's assume that the starting point is Reykjavík. Depending on how much time you have, there are plenty of places to explore that can take the whole day if not more. I would start by going on a ring road on the way to Hveragerði, and then on to road 39 to þórlákshöfn and Eyrarbakki. There you have a chance to explore caves right underneath the nearby lava fields. I would like to mention two caves - Raufarhólshellir and Búri cave. The latter one was discovered only 10 years ago and is probably the most beautiful one in Iceland. Be sure to have good hiking boots, torch and helmet. Take some extra LED torches with you to light up the scene for photos. If you´re done exploring the caves, follow the road 427 until you reach turn to Kleifarvatn (road 42). It's a stunning lake with great views for sunrise and sunset photos. Be sure to explore the nearby rocks, and you can find some interesting formations.
Right next to Kleifarvatn is a geothermal area of Krysuvík with mud pools and hot springs of many colors that are great for photography. For some extra cash you can dive in the lake and explore underwater hot springs.
After reaching Kleifarvatn, turn back on to road 427 and drive until the turn to Krýsuvíkubjarg. A short gravel road will lead you up to amazing cliffs right on the edge of the sea. You can explore the area a bit and marvel distinct red coloring of these cliffs.
By this time you should be reaching Grindavik, a small fishing village where you can stop to have a bite and look around. Just west of Grindavik is Brimketill, a lava formation by the ocean that look like a pool. I would also recommend exploring the lava fields around Blue Lagoon, for example crater row of Eldvörp is a great place to visit. If you follow the road 425 along the coast, you will reach another geothermal area called Gunnuhver. A place with huge steam vents spouting hot air and water. Little further down the road is a turn to another set of ocean cliffs - Reykjanestá.
These cliffs are extremely photogenic and is one of my favorite places on the peninsula. While on the road, you can also stop by fishing villages on the coast, all the way up to Gardur. Its the most western tip of peninsula and you can end the trip by taking a photo of a lovely lighthouse.