Don't know if this would be helpful but ...
There’s the Great Mall in nearby Milpitas. To the east and south are outlet centers in Livermore and Gilroy. To the south you have Santana Row in San Jose. San Francisco has Union Square. Across the nearby San Mateo Bridge is the Stanford Shopping Center. To the north is the Vacaville Outlets in wine country.
There’s the Computer History Museum in Mountain View. Intel has a small company museum on their campus. Winchester Mystery House is also in San Jose. Various museums in San Francisco such as The Asian Art Museum, Contemporary Jewish Museum, Disney Museum in the Presidio. Lawrence Hall of Science is in Berkeley.
As was mentioned, there is Alcatraz which you get to via ferry from the San Francisco Ferry Building. From the same building, you can also take a ferry to Angel Island.
Of course there’s the usual famous tourist attractions such as the Golden Gate bridge you can walk across. Also there, Coit Tower, Golden Gate park, Presidio, the fort under the Golden Gate, Fisherman’s Wharf, Yerba Buena Gardens. In Oakland, there’s Jack London Square and Hiller Aviation Museum.
The various wineries in Napa and Sonoma can take take a day at least esp if you also take the tours. However, you might want to check beforehand because of the fires. The Charles Schulz Museum is in the area in Santa Rosa. There’s also wineries in the Livermore area.
For the wagering sort, there’s various card rooms in the Bay Area. There’s also various Indian casinos in the area which have shuttle buses to and fro. I believe there’s some that leave from the Fremont BART station. In Emeryville, there’s a horse track that offers $1 Sundays.
There’s several universities in the area if a few want to tour schools. Keep in mind a few may be in finals during that time.
There’s baseball games and maybe the Warriors will still be in the playoffs still.