Before the road, the way out of Saksun was on foot over the ridge to Tjørnuvík on the next fjord. The old postal route is still walkable and is one of the most rewarding day hikes in the Faroes. It is about 7 km one way, climbs steadily to around 600 m, and takes four to five hours with photo stops.
The path leaves the village heading east, climbs through grazing land and then up into rougher terrain. From the high col the views open out over both fjords — Saksunarfjørður behind, Sundini ahead, and on a clear day the islands of Eysturoy and Kalsoy strung out to the north. The descent into Tjørnuvík is steep.
You'll need a car at both ends or a willingness to retrace your steps, since public transport between the two villages requires a detour through Torshavn. Cloud comes in fast over the ridge — carry waterproofs and don't start in poor visibility.