The next morning we got up pretty early (well, it never really got dark... I never did get past waking up at 5am, seeing the bright sun, and thinking "I must have overslept!"), and went down to explore Torshavn and work out some SIM cards[1].
One of the reasons that Torshavn is the major city is that, in a set of islands with steep fjords and cliffs, it's one of the few places where they could make a modern harbor. It's quite nice, especially since there were more boats than normal due to a regatta.
[1] Vodafone.fo has possibly the best SIM package on the planet, BTW. Our SIM cards cost us $9 each. Each had 5GB of excellent 4G coverage everywhere in the Islands, including the tunnels and the remote villages. Plus, the SIM had 4GB of roaming coverage in Europe, the UK, and Island. So yeah, pretty much all the internet both of us could consume for $18.