Firstly, be aware that August is ultimate high season here in the Algarve.
Most of the beaches will be full and if last year was anything to go by much of the reasonably priced accomodation witl be heavily occupied.
There are essentially two areas you should try:
1) Around Tavira in the Eastern where there are some good beaches .
2) Around and to the West of Lagos in the Western Algarve.
In Lagos we have Meia Praia, a beach with 4 kms of golden sand. Lagos itself is great having culture, history and a great nightlife.
West of Lagos, you can consider the following places and beaches:
Burgau,
Salema, (Lovely fishing village)
Praia da Ingrina (Turn left at Raposeira)
Sagres - several lovely small beaches
Praia Amado - Beach (via Vila de Bispo)
Carrapateira (On the Vila de Bispo Road)
Be aware that the Algarve is not big and with the dorsal A22 motorway running the length of the region you really can be anywhere in the Algarve in under 2 hours.
As regards accomodation you may find ti difficult to arrange a place for less than 7 nights as in high season most self-catering is renting out on this basis. B&B's etc will also be full.
Have a look at my blog
http://barlaventostravelblog.blogspot.com/
and the links on the top right panel headed:
algarve_property_rentals
I know all these operators and am sure that on of them will able to assist you.
For these, fell free to quote my blog if you think it will help.
Also have a look at:
http://www.algarve-web.com/rosamontes/default.asp
This has also been taken over recently by a company I know.
They all offer accomodation between Meia Praia, Lagos and Sagres and may be able to help.
