Camping by the sea in Gran Canaria isn't easy as most campsites are up in the mountain, but at Playa de Vargas the tents are just behind the beach. However, this isn't not a spot for sun worshippers due to the consistent east coast winds. Vargas is where windsurfers and kitesurfers stay to be as close to the water as possible. It has wind and waves and is a popular spot for wave specialists.
That said, Playa de Vargas can be pleasant during the winter when the east coast winds are at their weakest; Especially if you bag one of the stone sunbathing shelters. Visit when the tide is out and you even get a strip of sand between the sea and the pebbles.
If you visit Playa de Vargas to sunbathe and swim, please look out for the signs and avoid getting in the water in the windsurf areas.
Playa de Vargas is just south of the airport in the Ingenio municipality. The easiest way to access it from the GC-1 motorway is by turning off at exit 25 (see directions here). You can park right by the beach.