There is a lot between 12th and 14th on Jefferson St. that is a safe multi-story lot which is $12 if you are in by 9:30 AM. I believe it closes at 8 PM. It is right across the street from the Federal Building. It is not a terribly far walk.

BART will cost you $4.60 RT from El Cerrito Del Norte, plus if you aren't there by a little after 7 AM, the free part of the lot will be full. You can buy a daily reserved space for probably $4 or so, in advance, and you can be there up until 10 with that pass. (After 10, those spaces go to anyone).