If you don't mind getting sand in all your creases, Tarifa will do you fine, but Tarifa is really for active watersport enthusiasts than beach people. It is also situated at the junction between the Atlantic and Mediterranean, which adds some novelty value.
Be prepared to be surrounded by people that say 'dude' and think shark tooth pendants are cutting edge fashion.
Check out some of the super-cheap rooms and apartments you can rent in Tarifa on Airbnb (book direct).
Next beach >> Gandia, Costa Blanca