The airport and its cafe used to be very homely, but if you have a little time and are catching the Strandfaraskip Landsins bus from Torshavn, stay on it past the airport and go down to the village at the end of the runway, Sørvágur. It's got a lovely harbour, beautiful views over to Mykines (The Faroes most mysterious island) and if it's open a great cafe called Fjørðoy on the ground floor of the Hugo guesthouse. I think the airport hotel Hotel Vagar has a cafe, but it can be busy if, as happens sometimes all of Atlantic Airlines flights are delayed by the weather. I remember being delayed by 72 hours one November, Atlantic's planes were stuck in Stavanger, Bergen and Reykjavik...but somehow in a miniscule gap in the weather they managed to fly all three in within ten minutes and fly them back out again within the hour.