The Univsersity of California possesses a wonderful botanical garden. Tucked up the hill from the stadium, it houses a great number of plants native to California, as well as several international and special exhibits. This includes a succulent house, holding cacti and other succulents from around the world, as well as a tropical greenhouse with exotics from Asia and South America. On the far side there is a separate section dedicated to redwood ecology.
There is a pond and a creek running through the area, and it is a fabulous place to wander. Bring a camera, especially in the spring when everything is in bloom. You don't even feel as if you're still in the crowded Bay Area.
Admission prices are as follows:
Seniors (65+) $5
Juniors (13 - 17) $5
Children (5 - 12) $2
Children (under 5) Free