When we arrive at Vágar Airport (FAE), will there be an ATM in the airport? (If not), what about the nearby town of Sørvágur?
A DuckDuckGo search for
ATM locator shows many options. Above is the second hit. First hit was Visa and it said there were none in 600 kilometers of either of your locations.
You can also see them on Open Street Map, or if you want a list, see https://stackoverflow.com/questions/23684689/open-street-maps-query-for-atm
There used to be an ATM at the airport, but I am actually not sure if there still is one in the new terminal :-) See: https://www.youtube.com/watch?v=MsKqPSE65RI
But there are ATMs both in Sørvágur and Miðvágur near the airport.
And if you are traveling to Tórshavn with bus, there is one at the busterminal.