Thanks everyone for the helpful info! I called around and it seems like you can only donate the cord blood if you are delivering at Alta Bates. I can't believe that as progressive as we may think we are here in the Bay Area, there aren't any other options.... I will keep you posted if I learn anything more.                
                             
        
Re: Follow up to cord blood donations
Ok, I just did a quick search. This is also an option:
https://parentsguidecordblood.org/content/usa/banklists/publicbanks_new.shtml#LifebankUSA
Photo by Zemya Photography