Gjógv is a good base for exploring northern Eysturoy and the neighbouring islands. The drive south to Tórshavn takes about an hour, passing through the Eystur sub-sea tunnel under the sound.
Kalsoy — the "flute island" — is reached by ferry from Syðradalur on Kalsoy's western coast, about 35 km south. The hike to the Kallur lighthouse at the northern tip is one of the most photographed walks in the Faroes, with near-vertical cliffs on three sides and views across to Kunoy. The ferry is small and runs infrequently; check the timetable before you go.
Vidoy and Bordoy — the linked northern islands — are a 45-minute drive south and then across to Klaksvík, the second-largest town in the Faroes and a reasonable place to stop for provisions and fuel. From Klaksvík the road continues north through Norðoyatunnilin to Vidoy and Bordoy, with dramatic sea views and the Múlafossur-style cliffs at Enniberg on Vidoy rising 754 metres from the sea.
The coastal hiking trail west from Gjógv toward Tjørnuvík — a walk of four to five hours — leads to another photogenic village at the foot of the sea stacks Risin and Kellingin (the Giant and the Witch), two of the most recognisable formations in the Faroes.