The Faroe Islands is one of my favorite places I've ever been. I went in October 2014 for an extended weekend (4 nights) -- something which is eminently doable for Americans if your city is an Iceland Air gateway. I arrived in KEF and had around 4 hours between flights to make my way to RKV in a taxi (note: that ride is about $120 USD one way; there are cheaper ways to do it via bus). On the way back, I had a similar layover but Atlantic Airways actually flew into KEF that day.

I have never smelled air so clean and fresh as in the Faroe Islands. An awesome and unique destination. Once was enough though, at least for me.