These are excellent nearby hikes if you're in San Jose on business and you've got a free day or afternoon before your flight. A quick look at the hike locales:
Santa Teresa County Park: Right on the rim of San Jose, this park gives an excellent wildflower show every spring.
Almaden Quicksilver County Park: The attached guide passes historical relics of the era when San Jose had one of the world's largest mercury mines.
Calero County Park: Nice place to hike if you don't mind the horses.
Uvas Canyon County Park: This one is farther afield but the waterfalls there make it the best of the bunch.
Don't forget your sunscreen: these hills are very sunny.
It may be too hot to hike here in the summer unless you get off to a very early start.
Uvas Canyon can be chilly first thing in the morning; dress in layers.