There are quite a few areas where we have wildcamped along the La Manga strip, seem to remember a nice little place at the 10km marker (all along the strip they have surf boards with the kilometre on it. If you drive right to the end just over 18 kms there are a couple of largish areas where you can park. There are few areas before you go along the strip such as at Mar de Cristal. It is about 4 years since we were there but we are hoping its still ok. Make sure that you are stocked up with supplies if you are going to the end of the strip because there aren't many places open. We are hoping to be down that way in mid March.
There is the Camping La Manga, we have stayed on there a couple of times but it is a bit marmite, some people love it others can't stand it but as we wanted to use our inflatable canoe it was nice to leave it set up & get out when ever we fancied it.