Our hotel is in the center (big white building). Because of the eclipse, it was very hard to find accommodation even three months in advance, and all the prices were inflated. I was able to get a room here, in Klaksvik, for the eclipse. Then after the eclipse we went to the "big city" Tórshavn, the capital. This suited us fine. We got to stay in a smaller, more out of the way (if that's even possible here?) place first, before going to the more typical tourist area.
The hotel was running lunches for tour bus groups, and they let us eat there too, as it turns out for free! They are just so very nice there! We would never have dreamed they'd just let us partake of the buffet just because we were there -- we were anticipating a nice charge for an overpriced meal, cynical, world-wise travelers we are, so we only ate there twice, once when we'd just arrived, and one day when we were too tired to find something else...