Since I moved to the Bay Area, I have only visited a few places within the limited time I had. I know I really should be visiting more places that may be within 6 hours drive from where I am.
As it can be noticed, I have a page on cars and enjoy driving to places. So most of the neat places were discovered accidentally on my way somewhere.
There's a neat mountain road going past downtown Saratoga. Maybe it's called highway 9, I forget. It only has a lane on each side but it's rather fun and before you know it, you get to some crossroad in the mountains. Nearby there was one, maybe two places where you can park and see the lights of the city and you'd be close to Palo Alto and maybe Woodside.
Another neat place is in Santa Cruz. I got lost but knew which side the shoreline was, so I kept driving until I found a small beach just under a cliff with some parking space. I still don't know where it is on the map exactly, but have been able to visit it a few times.
One neat but scary place is going east on Calaveras. The road goes uphill by some country clubs and then seems to go to the other side of the hill, or is it actually a mountain? Anyway, the view beyond is breathtaking and dangerous at the same time. There are some places where one can physically stop without blocking the little but pretty much invisible traffic. However, they tend to be right in front of some sign prohibiting loitering and/or tresspassing, posted by the landowners I presume.
About 10 minutes drive from the Berryessa exit off 680(280) is Alum Rock Park. There's a parking lot at the foot of the hill where you can pay a toll to go up by car. I have yet to trek 'till the end,' but walking 45 minutes gets you to a location with plenty of places to sit around, play and barbecue. It seemed like that was the last location one can go by car and park. Beyond that I have no idea. I didn't check a map but somehow made it back; however, I suggest you do to avoid taking routes that may take you to the same place one started at or to a totally different exit. I was able to see 2 deer on my way down and they didn't freak out on me.
It took about 4 hours drive from San Jose to Yosemite National Park. I took the route through Gilroy on 101 going, and the route coming up through Stockton and 580. I heard a lot about it, but was finally able to see for myself what made it famous. Once there, it took roughly 1 hour to get to Vernal Falls with a couple short breaks in between. The next one would have been Nevada Falls. Time and physical limitations led me to call it a day. I was still able to see part of Nevada Falls and went just a bit ahead of 'the bridge' from which it could be seen. At that point it was probably a 2 hour trek, not counting any break time. I'm not used to seeing this much natural splendor without trekking over 3 hours. I think this is a deal. In between there's a 'pool' just ahead of Vernal Falls where people tend to take a lunch break and kick back for a while. Being Fall, there wasn't as much water as in cooler seasons so one can walk over the pool surface (some visitors wipe out and slide into the pool). There's a $10 fee at the entrance that is good for 7 days.