The tourist information office, opposite the beach in Playa arena which is a short walk from Los Gigantes, has a lot of information about walks, transport etc.
You can't miss the Masca walk. The staff at the Nashira Uno office located by the barrier into the marina can arrange this walk for you. A mini bus takes you there, you walk down the barranco with a guide and their boat brings you back to Los Gigantes.
Another very pleasant walk is to follow the coast to Alcala, enjoy lunch or a coffee in Alcala square. You can walk back again or hop on the local bus.
Hope you enjoy your stay. Do report back and let us know how you got on.