The Monterey Peninsula is not known for its surfing but there are a few spots you can go to and catch some moderate waves. For some of the best and high breaking waves, head north to Santa Cruz - also known as Surf City, USA.
Spots to consider: Asilomar State Beach, Lovers Point (watch for the rocks), and Carmel Beach.
Two things you probably already know: Surfing can be dangerous - always surf with a buddy. Secondly, the water here is REALLY cold so you will need a wet suit.