Here is another blog post about a beautiful lookout in the southern part of the island. Driving on FV-605 from La Pared to Pajara, you will reach after half the distance the Mirador Astronómico de Sicasumbre.
Fuerteventura is a light protected area. This concepts involves the minimizing of artificial light sources, especially outside of towns and villages, so you can watch the stars at night without disturbing artificial lights like street lamps. For people who like watching stars and planets Fuerteventura is an El Dorado. But even if you usually don’t pay attention about astronomy, you will realize that you will see more stars and even the milky way.
We were twice at this lookout and the view is fantastic. It almost looks like someone painted the landscape. The actual viewopint is a five minute walk from the parking lot uphill, so I would recommend to wear suitable shoes. From up here you have a wonderful view over the western part of Fuerteventura, which is barely populated.
Here are some impressions from our trip:
View from Mirador Astronómico de Sicasumbre