I don't know about quads in Playa Blanca but MegaFun in Puerto del Carmen offer 3 hour treks out in quads or buggy's over to Famara and back. You need to have a driving license, its mostly off road and great fun!
http://www.megafun-lanzarote.comAnother alternative is the Segway hire, they do operate from Playa Blanca and again lots of fun around the resort, to Papagayo or up in the Femés mountains.
http://www.ajaches.com/Have fun!!