Reykjavík, the world’s northernmost capital, and it is also one of the smallest in the world. It is easy to find your way around and it is a friendly city that offers a surprising amount of things to see and do. Reykjavík is a amazing green and sustainable city close to pure nature.

1. Perlan - The Pearl
Perlan is built on 6 water tanks and each one of them contains around 4 million liters of warm water.  In the middle of Perlan is a hot spring (geyser), but there is also one outside. On the 4th floor, guests can go out on a balcony and see the spectacular 360 view of Reykjavík. Perlan is an educational site as well. It host The Glacier Exhibition of Iceland, a 100-metre long ice tunnel, and with unique information about the glaciers in Iceland.
Perlan in Reykjavik Iceland
2. Kolaportið  -  Flea market
Reykjavík‘s only flea market is located in the city center near the harbour. There you'll find all kinds of people selling many different things new and second hand, old things, Icelandic homemade sweaters, records etc.  Also the traditional Icelandic food. The market is open only on weekends.
Swim with the locals in the sea at Nauthólsvík in Reykjavík - A&R Photos
3. Swim with the locals in the sea at Nauthólsvík in Reykjavík
Would you dare to swim in the sea where the water is around -1° C and dressed in my best ballroom dress? Well if you do then you can do that in Iceland  because it is a popular traditon with the locals on a New Years' Day. The cold water shocks the body and it is said that it is great to take a hot bath afterwards. You can play volleyball on the beach and play in the sand or go for a swim. The water is heated during summertime and the water should be around 18° - 20°C (64° - 68° F). Remarkable experience  that  you will never forget!
4. Look for elves, hidden and mystical people in Iceland
You can take a tour in Iceland to look for elves and hidden people. Many Icelanders firmly believe in those supernatural phenomena and it is an inherent part of the Icelandic culture. Elves hidden people can be found all over Iceland and even in Reykjavík. There is even a possiblity to attend the Icelandic elf school to learn about the all the different types of elves, trolls, gnomes, fairies and dwarfs. It is different experience to walk into a world of the Icelandic elves and hidden people and get to know there hidden life. More information.
5. The capital's Mountain - Esjan
Gives you a spectacular view from top Esjan is a very popular mountain among hikers and climbers. The most popular hiking route summits to Þverfellshorn. You do not need to be in the best shape to climb the mountain, you can always go back if you get too tired. It takes around 3 hours with easy walk from bottom to top and down again.When you climb Esjan, you would have to take the weather into consideration. It is not preferable to walk during winter, but during summer you could walk day or night. You would need to wear good shoes, and it‘s good to have breathable trousers and jacket. 
6. Imagine Peace Tower
Imagine Peace Tower is a memorial of John Lennon from his widow Yoko Ono situated in the Island Videy, right outside of Reykjavik . The peace tower was lid up on the 9th of October 2007 for the first time. Yoko Ono, Lennon's widow, gathered wishes throughout the years that are buried underneath the memorial. The words "Imagine Peace" are written on the memorial in 24 languages.  The Tower is lit from 9 Oct – 8 Dec, 21-31 Dec, 18 Feb & 20-27 March. The 9th of October was John Lennon's birthday, and the 8th of December was the day he got shot.
7. Klambratún, Park
Klambratún is a large park in Reykjavík which offers a variety of activities, like volley ball, frisbee golf in the city center. The large park is sometimes used for concerts or entertainment and has been used on Cultural Night and like everything on Cultural night, there is free admission. 
8. Laugardalur, the Valley
Laugardalurinn is a valley in Reykjavík where in the old days, women washed their laundry in the hot water which came from the earth. A bit odd dont you think? There you can find the Botanical Gardens, a fairytale like garden, with around 4000 plants,  a sportstadium and  marked running paths. It is a great place if you want to enjoy the outdoors in the city. One can visit the valley anytime.
9. Northern Lights or Aurora Borealis.
A Free show of the nature. The most magical free thing in Reykjavík are the beautiful shows of the northern lights. The best time to spot the aurora borealis is from fall to spring on clear nights. It is a spectacular and breathtaking phenomenom. Here are some guides seeing the Northern Lights from Reykjavik.
10. The Midnight Sun
Try the sleepless nights on Reykjavík during the Summer solstice. You cant sleep anyway as you want to capture the midnight sun that creates shades of pink and yellow all around the city. You can literally feel the extra energy fuel your body at that time.
Reykjavík City Card
The Reykjavík Welcome Card is the easiest and most inexpensive way to experience the city! The Card offers free entry to a great selection of museums and galleries, all swimming pools in Reykjavík and free unlimited travel by bus within the Reykjavík Capital Area. In addition, the card also gives you a free ferry trip to Viðey island and discounts on various tours, in shops and on services. Reykjavík Welcome Cards are available for periods of up to 24, 48 or 72  hours.