Fanime isn't the only major anime convention in Silicon Valley anymore. AOD (Animation on Display) takes place next weekend and features two days of Japanese animation, video games, cosplay, and other geeky attractions. AOD will be located at the Santa Clara Convention Center with easy access from Light Rail (there is plenty of parking as well).
It's worth noting this event previously took place in San Francisco until 2013. Last year it migrated down to Burlingame, and this year it finally made it to the right region.
You can view a full list of events and exhibits at the AOD website over here.