I've surfed a lot of places starting when I was a teen. It looks like you're in The City, so I know you'll want to check out Ft. Point - which I like - right under the Golden Gate Bridge.
Other places are down in Santa Cruz. Here are the best of the best: Pleasure Point (East Cliff Drive at 30th); The Hook; Steamer Lane; and Four Mile (4 miles north of Santa Cruz). Guys are very territorial and if they think you're from the Bay Area instead of local - they might give you some shit. Just stand up for yourself and don't take crap off any of the local tough guys. They don't own the beach (they just think they do!) My old GTO once had license frames that said "Palo Alto" where the dealer was located. I took those off and had no more accusations of being "Valley" from anyone. Have fun. A full wet suit is needed, as opposed to a short one - for SoCal beaches).