Are you new to the area?
There are numerous farmers markets all over Bay Area, including the East Bay. The San Francisco markets are worth checking out, especially the market in Alemany. A quick google will give you any info you need. All the farmers markets are listed on their own or affiliated websites.
The Berkeley markets tend to be expensive and boutique-y. They are as politically and nutritionally correct as you can imagine. I know vendors there, and they've told me about the organic requirements for the food, the ecological requirements for packaging, etc etc etc etc etc etc etc etc etc etc etc...Parking is difficult, if you want to do it legally. The Saturday market in downtown Berkeley is accessible by BART. I still go to the Berkeley markets anyway, for unusual and excellent produce--just not every week. I don't have a favorite for any one of them.
The Oakland markets are more reasonable. The Friday market in Old Oakland sells a great deal of Asian produce and I like to go there. It's accessible by BART. A cooking teacher I know likes the Grand Lake market. A foodie friend has recommended the Temescal market to me.
The Kensington market is smaller, but friendly with very good if not excellent vendors. I like this one and I'll shop there if I'm passing through the area. Parking is less nervewracking than it is at the Berkeley and Oakland markets. That's not saying much, though.
good luck with your shopping, and parking if you're driving...