Tinganes
The Faroese have one of the oldest parliaments in the world, located in the Tinganes section of the capital city of Torshavn. Their parliament first met during the Viking ages in 825, and is in good company with other old parliaments such as that of Þingvellir in Iceland and Jamtamót in Sweden. The buildings still standing here today are from the 16th and 17th centuries.
Walking around Tinganes in the middle of a fine Sunday I discovered two things: 1) It's pretty darn small. You could see the whole thing in 5 minutes if you wanted. And 2) Like elsewhere in the Faroes, you're not likely to encounter a lot of other tourists (yay!). If you take a visit to Torshavn, it's pretty hard to pass up walking through this small and enjoyable historic area, easily accessible from downtown Torshavn on foot.