Our City Forest is a local nonprofit organization which plants and maintains trees in the City of San Jose, and engages in environmental education. Their main office is at 1590 Las Plumas Ave, 95133.
They also maintain a community nursery, located at 1000 Spring St. San Jose, CA 95113 (off Hedding, near the airport). The nursery hosts classes and workshops, and offers tree seedlings and other drought tolerant plants in exchange for donations. It is open Thursday - Saturday, 9am - noon.
To volunteer, or for more information, see their website, http://www.ourcityforest.org/