Cave hikes are found only in Pinnacles National Monument, about 90 minutes south of San Jose.
Pinnacles National Monument
At Pinnacles, there are two cave trails (Balconies Cave Trail and Bear Gulch Cave Trail) that require flashlight. The caves are open only in select months, so check Cave Status. Caves are closed for the protection of Townsend's big ear bats that reside in them. They are open for a limited period: twice an year for at least one week and up to four weeks each March and October, depending on the presence of the colony of bats.
Pinnacles is generally hotter than San Jose. So avoid summers. Spring and Autumn are good times for cave hikes. In spring, wildflowers bloom.