Castle Rock State Park - Los Gatos is a beauty nestled in the Santa Cruz mountains with lots of interesting rock formations. There are areas for hiking, camping and rock climbing. There is free parking on the highway if you don't want to pay to park in the lot like most other people. Just across from Castle Rock and to the right is another little park. Don't fuss with that hiking, but do follow the signs for the rock formation not far from the entrance. When you climb on top you get a great view of downtown San Jose.
Santa Teresa Count Park - San Jose located in South San Jose not too far from downtown. It's filled with rolling hills and views of the city. If you catch it at the right time you can find the hills covered with wildflowers. The hiking is fairly easy just watch out for SNAKES!
Calero County Park - San Jose is located in between South San Jose and Morgan hill. It offers about 20 miles of hiking and horseback riding on some rolling hills including some loop trails. There is also a reservoir for boating activity down the road. The hiking offers nice views of the area as well as some high dollar houses. The only real danger here (aside from stepping into a giant pile of horse poop on the trails) is running into some wildlife. We saw a pair of coyote running on the hill ahead of us and a deer on our first trip, but noticed many fresh tracks of bobcats and mountain lions. I cannot at all recommend going out by yourself. That is also the reason they close at sun down - predators come out to play after dusk!
Uvas County Park - Morgan Hill is nestled outside of Morgan Hill. You will have to drive through a small Swedish community on a narrow road just before the park. There is an entrance fee and a few parking lots. There is a waterfall loop trail that is pretty easy walk. They are not the typical waterfalls that I think of, but they are pretty non the less. We also hiked up to Knibbs knob peak. It's a pretty steep climb up a dirt path. It gives you some views of the evergreen covered mountains. I wouldn't say it' breathtaking beauty, but it's a good workout
Water way at Uvas Canyon County Park in Morgan Hill
Overlooking the city of San Jose at Santa Teresa County Park - South San Jose