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Hi Tessa,
there are not many places to do wild camping in the Portimão area since it's a city with lots of people. If you look at the area of Lagos or Sagres is easier. Farther west you have beaches like Boca de Rio, Amado, Bordeira where wild camping is possible (which is not legal in Portugal - attention). If you are without a car and want an easier way to travel and know several beaches in the Algarve and have a good place to sleep you can opt for a campervan. Take a look at https://portugalbyvan.wordpress.com/

Cheers.

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Hello Tessa,
The west coast and places like Salema (east of it) are pretty good for wild camping. Not the heavily built Portimao with its many golf courses, people are also not mindsetted for it.
Try to do it a bit hidden; no colours like the campervan recommended by Golden Sunsets though it should be a good option because he/she is recommending it in 100% of his/her posts.

Why wild camping? I assume it's also a money factor?!

Nb. If you should consider a campervan, make good inquiries about the type of insurance. It always gives extra payment.
Nevertheless, I don't recommend (reason to be found in all my other campervan posts).