Can I Fly A Drone Here? Like If I Take A Mini-Hike With My Friends Up Here? Can I get some drone footage shots up here? Or is it still FAA Restricted Airspace, I'm pretty sure it's far enough from the airports...

No, drones are not allowed in San Jose regional parks.

I am not sure whether you may fly a drone in the valley of Alum Rock, but rugged landscape will be a big problem for you to control it by RF...

EDIT/UPDATE: Short answer- no. Just called the Park Rangers and they confirmed no drones allowed. They said most National/State Parks don't allow drones anyway. Long answer: It's definitely outside the 5-mile-within-airport-radius (FAA restriction), so that won't be a problem. The problem though is if it falls under the National Parks ruling, any aerial craft is prohibited without special permissions. Also, what Ted said: hilly terrain interfering with your signals.