If you’re at UC Berkeley with a little time to spare, go visit the Valley Life Sciences building and say hi to the sabertooth cat fossil there.
Smilodon californicus is our official state fossil. It got the honor from its abundance in the tar pits of Rancho La Brea down in Los Angeles. It turns out that they were suckers, walking into the tar to feed on animals already stuck there, then getting trapped themselves. They and the extinct dire wolf are the two most common species in the tar pits.
Presumably they lived in Oakland, but I don’t see any reference to local Smilodon fossils. One of the things on my to-do list is to visit the paleo people at UC Berkeley and learn more.
Oakland Geology 
16 February 2013 at 1:32 am
i’d check the san ramon valley museum. they did dig up some 8-10 million yr old fossils in the san ramon/blackhawk area in the 1930s and again in 1994-5. apparently, there’s a lot more there too. there were ancestors of sabretooths dug up along w/ ancestors of mastodons, hyenas, dire wolves, etc… found there. they don’t seem to feature this fascinating stuff at the museum very often – preferring recent history stuff to prehistoric stuff for some reason, but i think the stuff is still in their collections.
16 February 2013 at 2:04 pm
The museum (which I didn’t know about!) had its fossil show a while back, and apparently the specimens were loaned by the UC paleo department, which did the dig at Blackhawk. The museum seems to have a mastodon jaw on site plus some shell fossils.