The oldest part of Torshavn, called Tinganes is on a tiny peninsular of land that juts out into the harbour, and the 'streets ' are tiny, so small that you cannot get a car down them. All the buildings are of wood and stone, and they all have grass roofs. It's easy to imagine that nothing has changed in this part of town for centuries, and I hope that it won't for centuries to come.
The rest of Torshavn is a bit more modern, but still quite low rise, and rather spread out. It does have some great views across the water to some of the other islands that make up the Faroes, and a busy port with a constant stream of ferries coming in and out of the port. But the one thing it isn't is busy. I can't say that I saw any kind of traffic jam while I was there, and not that many crowds of people. Even the SMS shopping mall wasn't jam packed with people.
Torshavn (and the Faroes in general) is rather expensive, even a (very nice) room in a hostel was £50 a night - now that's not New York prices, but it's a lot of cash! The only way that you can eat on the cheap is to visit the supermarkets.