If you are in the Bay Area and have the time, it's worth a trip up to San Francisco. Located (NUMBER HERE) from the Santa Clara based Madison Street Inn. You can choose to drive or take the nearby Santa Clara Caltrain.
The train ride up takes approximately 1 hour and the final stop drops you off at the Embarcadero Station.
From there you can walk to Union Square, catch a bus, rent a bike, or catch an Uber/Lyft to any of San Francisco's iconic sites such as China Town (Free tea tastings in most tea shops), Fishermen's Warf (try the clam chowder) and North Beach with its many restaurants and Italian heritage. San Francisco is hilly, but walkable and is perfect for urban hikes.
Important Note: If you plan to go on an "on island" Alcatraz tour (highly recommended!) please plan to book at least one month ahead for best pricing and availability through the official website: https://www.alcatrazcruises.com/tour-options/
Other Parts of SF and the East Bay
You can also choose to transfer at Millbrae Station and ride the Bay Area's version of metro, BART (Bay Area Rapid Transport System) to access different parts of the City as well as Berkeley, Oakland, and the East Bay. A separate ticket is required to access BART which you can buy at the station.
Madison Street Inn, in Santa Clara, California can provide complimentary reloadable BART cards, that you would then fund yourself at the station. This may turn out to be faster and more convenient for you than buying a paper ticket every time you ride. Of course, these cards are yours to keep for the next time you visit the San Francisco Bay Area.