Hi. I'm also new to drones, flying since August, and live in the East Bay too. I recommend Cesar Chavez Park in Berkeley. It is adjacent to the Berkeley Marina and under the control of the City of Berkeley. Huge open area, very popular with kite flyers - especially on weekends. The large picnic area is popular with drone flyers, and model airplanes too. I recommend week days to avoid the kites and folks having picnics. The north area is an off-leash dog park so that's not a good spot. Also the shore lines adjacent are under the control of the East Bay Regional Park system - which has banned drones, there's also a State Marine Park to the north of Albany Beach, which is a no drone area under State Park rules.
I found Cesar Chavez park a great place to learn to fly, especially when its not crowded during the week in the early morning. Visibility is excellent and you're right next to the Bay and a cove that you can practice longer distance flight without fear of flying over people or structures. Flying up to Golden Gate Field and staying offshore over the Bay for example. Due to the proximity of East Bay Regional Parks, I've noticed on weekends that their Park Police helicopter will patrol this airspace at low altitudes - usually on weekends when more people are out in these parks - so you need to keep an eye out for it when over water or the cove.