The small peninsula was the first part of Færøerne to be inhabited. The houses were made of drift wood, since there were no trees on the islands. Driftwood was because of this a precious commodity.
To walk with a guide among these houses is an experience you should not miss.
A nice day trip is to take the ferry Ritan to the island of Nólsoy. While just a few minutes away by boat, Nólsoy village is a world away from Tórshavn. The village is extremely quiet and rural, with a number of walking and hiking trails to enjoy. There are even options to stay overnight if you wish. If you do make a day trip of it, be sure to check the ferry schedule carefully so you know what your options are to get back to Tórshavn.
According to legend, this stone fort was constructed in 1580 by Faroese national hero Magnus Heinason to protect Tórshavn from pirates. It didn't work all that well against foreign powers, however: the fort was destroyed by the French in 1677 and again by the British in 1808. The fort was constructed in its present form by the Danish in the early 19th Century. The fort was also used as a command post by the British during World War II. Today, you can wander through the stone works, admire the modern lighthouse in its midst, and enjoy views of the area.
The Faroese Museum of Natural History is a nice diversion on a rainy day (and let's face it, there are a LOT of rainy days in the Faroes...) The interior is rather dark, but there are quite a few very nice exhibits on local animal life and plant life, as well as the geological history of the Faroes. There are also quite a few interesting skeletons and animal models that most children will find to be quite cool.
Entrance costs Kr 20 for adults, free for children under 15 years old. During summer, the museum is open Monday-Friday 10AM - 4PM, Saturday and Sunday 3-5PM. Off season, it's open Sunday afternoons only, 3-5PM . Group tours and appointments can be arranged; call the museum for details.
The building known as Skansapakkhúsið was built in 1749. It was converted from a storage building to the Løgmansskrivstovan, or Prime Minister's office. Unlike many seats of national power, tourists are able to wander around the grounds and explore the building if they like. The building is open to the public Monday - Thursday 8AM - 4PM and Friday 8AM - 3PM.
Want to impress your friends at the next cocktail party? The Løgmaður (Prime Minister) of the Faroe Islands is Kaj Leo Johannsen of the Union Party. He leads a governing coalition of the Union Party, the People's Party, the Independence Party, and the Centre Party.
UPDATE: The 2011 general election did not result in a change of Løgmaður, but did result in a rather eyebrow-raising coalition including the Union Party and the Independence Party. I always welcome any emails from those who know more about the current Faroese political situation than I. :)
The Kongaminni (King's Monument) is an obelisk built in 1882 to commemorate the visit of the Danish King Christian IX.
To be honest there's not much to the monument, the main reason for climbing the hill to here is to get a fantastic aerial view of Tórshavn.
Havnar Kirkja has been officially known as Tórshavn's Cathedral since 1990. While it will never be confused with St. Peter's in Rome, the wooden structure is quite pretty from the outside. During "office hours" (Tue-Fri 4:30PM - 6:00PM, Sat 10AM - 2PM), you can also enjoy the striking interior and very nice organ practice. Note the blue ceiling and the maritime theme of the decor.
One of the first landmarks you'll notice in the distance when you get off your bus or ferry is the copper dome of the Vesturkirkja. The church is quite new, completed in 1975. While the outside is quite impressive, it's also very interesting to see the inside, with its grey-white altar and beautiful organ pipes. The church is open to visitors Monday - Saturday 3PM - 5PM during the summer, shorter hours off-season.
Vesturkirkja, with it's pyramid shaped copper spire, can be seen from most of Tórshavn.
Opening times are limited and could change, so check with the tourist office before setting out. When I was there the church was open 3-5pm Monday to Saturday.
This wooden farmhouse was built in the 11th Century — the same family has occupied it since 1550, and the 17th generation of the family is still living in it. Wood is very valuable here (no trees) and wooden buildings are rare.
There is a great way to go to Kirkjubøur. It is a hike that will take around two hours over the hill from Tórshavn to Kirkjubøur. You can get the route from the Tourist Office. They have a small book 'Walking in the Faroe Islands'. You must make sure you get to the right starting point and from there just follow the cairns... you cannot miss them! From the hill you can enjoy great views of Koltur, Hestur and Sandoy.
At the end of the hike you arrive in Kirkjubøur, here you find the famous Olavskirkjan.
Tinganes, or "Parliament Hill," has been the seat of the løgting (the Faroese governing body) since the 9th Century. It's enjoyable to admire the turf-roofed wooden buildings from across the harbor, or to wander among the narrow alleys on the hill itself.
Havnar Kirkja is Tórshavn's cathedral, situated at the (main land) end of Tinganes.
It's open to the public Monday - Friday 4.30-6pm.
Although rather ordinary looking on the outside the inside is impressive, if somewhat garish in it's choice of colour scheme.
The Skansin Fort was built in 1580 to defend Tórshavn harbour, which was constantly subjected to attacks by pirates.
There's not all that much to the fort, but it's worth a look. There are some cannons are on the fort, and it offers some good views both of Tórshavn and across the bay to the island of Nolsoy.
On top of the fort is a lighthouse.
The Natural History museum consists of one room with displays about the geology of the island, and another with information on the animals of the islands, prodominantly whales.
Not everything was in English sadly, but the musuem staff are friendly and happy to explain things to you.