So lets get in to it. You land on the island of Vágar (Airport island) you should stay at least 2 nights there. First things first, before you get out from the airport just rent a car from there. drive yourself to the place where you are staying.
Let's assume that you arrive in the evening and probably you are tired from traveling to get here and you don't want to hike for hours. So my first destination would be Gásadalur to see the famous waterfall called (Múlafossur). On the way to Gásadalur you should stop at the small village called Bøur. Just look at the beautiful grass roof top houses with the beautiful view of Tindhólmur and Drangarnir islands in the distance.
Driving to Gásadslur you need to go through a tunnel, you'll see signs where the waterfall is. Park the car and walk for about 300 meters. Important that you close the gate when you go in so that the sheep don't go out. After that you can enjoy the view and take as many pictures as you like :) Bonus tip: Take a walk to the village and go try out a local soup from the small coffee shop called Gásadalgarður. They have the most delicious soup. Don’t forget to take a walk around the village and admire the cute houses that this village has.
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I have created curated maps and itineraries for travellers that want to travel like me.