Torrecilla beach:
Located at the bottom of the Town centre (Calle Malaga/Castillo Perez/Chaparil all take you down there) This beach has had loads of money spent on it to make the beach area  wider and deeper. 
You can hire sun-beds and umbrellas, and maybe even a pedallo. There are showers on the beach too.
The new promenade makes a nice walk along to Playazo beach, and now extends East past the plaza de la cangrejo.
There are two bar/restaurants right on Torrecilla beach.

Calahonda Beach

Situated immediately to the East of the Balcon de Europa, this is a small beach that is quite sheltered if there is a bit of a breeze, and although there are a lot of rocks to either side of the beach, the beach itself is quite sandy with a mix of small pebbles and sand.
The walk down is quite steep, but there is a bar restaurant that is open during the summer months, and there are sun-beds and umbrellas for hire.
Handy if you are in town and just fancy a quick sunbathe or just a beer by the sea.

Carabeo beach
 

There is a small cove just off C/Carabeo, and another which actually joins with Burriana beach , both are much less crowded than Burriana.