There is an amazing observatory on top of Mount Hamilton, which is accessed near the Alum Rock area of San Jose. There are multiple telescopes in the white domes, which can be seen from many of San Jose's freeways on clear days. If you go to the top in the daytime, you can see the smog line across the sky above the city. During the summer there is an event at which those who purchase tickets can look through the big telescope which is in the largest dome, and under which James Lick is buried.
You can't really tell from this picture but the approach road is very steep and twisting. Lots of people actually think it's fun to cycle to this place judging by the number of cyclists we saw on the road.
Up in the hills behind San Jose is the Mount Lick observatory. If this kind of thing interests you than its well worth as visit as you get inside the domes to see the telescopes.
It also has a centre for siesmic studies and this show just how frequent very small earthquakes are around the Bay area - at least one a day in the time period we saw.