For most of San Francisco Bay you'll have plenty of water under you and you won't have any problems in marinas or anchorages.
However, the farther inland you go the more draft becomes an issue. If you're going to cruise the Delta, a draft of 3-4ft or less is what you'll want. Even getting in and out of marinas can be a challenge. Many parts of the Delta and Bay are silting in at a rate of 1-1.5ft per year.
Keep this in mind when you look at charts.
That said, I draft 6.7ft and have gone to Napa and Suisun without any great problems. I always do a careful check of tide tables though.
What I'd recommend you do is look carefully at the charts for the areas you're planning on cruising. This'll give you an idea as to what draft you're willing to live with.
Skipper, J/36 "Zero Tolerance"
PS The vast majority of the Bay and Delta has a silt/mud bottom. When you do run aground, it's at least a soft bottom.