National Museum of Iceland

Perhaps the most important of the must-see museums in Reykjavik, the National Museum of Iceland has three floors containing thousands of items that tell the country’s entire history, from Viking-era sailing boats to modern airport designs.

Located next to a university campus, the museum features 2,000 objects, including suits of armor, ancient swords, and even an entire small nineteenth-century house. Plus, it houses Iceland’s largest photography collection, with 1,000 photographs from the twentieth century. It was even once home to the last surviving McDonald’s hamburger sold in Reykjavik.

Reykjavik Art Museum

Although it's called the Reykjavik Art Museum, this is actually a series of three interrelated museums. Hafnarhus, on Tryggvagata Street, combines contemporary art from around the world with a large collection of work by Icelandic pop artist Erró in an old harbor warehouse.

Kjarvalsstaðir, meanwhile, houses the works of perhaps the most famous Icelandic artist, Jóhannes Kjarval. Alongside these pieces is a modern art collection inside a modernist building on Flókagata Street — which many consider a work of art in itself.

Speaking of beautiful buildings, the Ásmundarsafn is one of Reykjavik’s best. It was named after sculptor Ásmundur Sveinsson, whose work is displayed inside and outside the striking, domed structure on Sigtún Street.

Reykjavík 871±2

This museum's weird name makes it sound like a pretentious art gallery, but, in reality, Reykjavik 871±2 is an innovative museum celebrating the so-called Settlement Age, when the first Icelanders came to the country.

The museum gets its name from the ruins of the hall at the center of the exhibition, which has been dated AD 871 plus or minus two years. It explores leading academic theories on what heritage sites such as this might tell us about life in Reykjavik centuries ago.

Icelandic Phallological Museum

Maybe not for everyone, but the world’s biggest natural phalli museum is certainly unlike any other Reykjavik museums.

The museum is home to more than 200 full and partial penises, including shockingly large whale genitals (a collection affectionately labelled "Moby Dick"), polar bear organs, and even a human specimen.

Saga Museum

Icelandic sagas are to Iceland what Shakespeare’s plays are to England — literature so iconic that it's a part of the national psyche. This connection with the sagas is celebrated at one of the best museums in Reykjavik, found on Grandagardi Street, where figures from the sagas and chronicles are brought to life using incredibly detailed models and replicas.

This is, however, only a small sampling of the museums on offer in the Icelandic capital. Wander through the city and encounter other attractions such as Volcano House, the Reykjavik Maritime Museum, or the museum-wide tribute to the "Whales of Iceland." All these and more are available for adventure-seeking tourists, so be sure to pack comfortable shoes.