My suggestions would both be in Fuerteventura.

Infiniti apartments - email them and ask to talk through what you want or Maravilla apartments if you want to walk naked from the breakfast table to the sea.
In both cases you will need to book your own flights and transfers but the Fuerteventura Forum had some very good advice on both subjects in existing topics. Additionally, I believe that Infiniti are able to arrange airport transfers these days.