Hornstrandir
Description
Hornstrandir is the northwestern peninsula. No people are living here any more. The area is declared a nature reserve. What you will get: deep sea inlets, birds, plants, immense cliffs with bird colonies. Near Hornvík is a large cliff with a busy bird colony.
Take a ferry, a tent, and have yourself dropped at Hornvik or another place. There are several hiking trails. Bring your tent and a good map.