Depends when you are coming!
If it is over summer you may have some real difficulty as most places are already booked.
There is limited accomodation in the Carrapateira area as building is strictly controlled.
You may find it better to stay near Sagres or Lagos and drive as it is only 20/30 minutes.
Try these sites:
- http://www.solpraiaferias.com/
(Sagres/Carrapateira & Car Hire).
- http://www.algarve-web.com/rosamontes/default.asp
(Near Burgau - Nice location)
- http://www.docemaralgarve.com/aurora.htm
(Near Burgau)