https://www.tripadvisor.com/Attractions-g60713-Activities-oa...
https://www.atlasobscura.com/things-to-do/san-francisco-cali...
The Tripadvisor ones are pretty much the definition of the beaten path, while the Atlas Obscura ones are pretty much the definition of off the beaten path.
Golden Gate Park has a kind of absurd amount of stuff within it. There are three different ways to get a good view from above (take the elevator to the viewing platform inside the De Young Museum, ride the ferris wheel, or walk to the top of Strawberry Hill, the island in the middle of Stow Lake), and there are lots of different gardens with different themes and focuses. Plus a dedicated roller skating court and a bicycle riding practice area. Well, I would be here for a long time if I tried to list everything in the park.
I personally really like the Japanese Tea Garden there.
Most people will tell you to go to Muir Woods to see the redwoods. While it's certainly incredible and very worth it, it can get crowded because so many people want to see it (there are restrictions on parking and I think even the bus might require reservations nowadays). Two other great redwood forest areas (among many!) that are less visited are Samuel P. Taylor State Park (in west Marin) and Reinhardt Redwood Regional Park (in the East Bay Hills).
In general I think the East Bay Hills are underappreciated. They have a complicated tapestry of (quite enormous) parklands, suburban sprawl, reservoirs, and tiny towns with distinctive cultures, also interspersed with great views. They are fascinating to bike through, or over, if you're in good shape.
If you do like riding a bike, Marin County (north of San Francisco, on the other side of the bridge) has wonderful scenic bike routes of all distances and levels of difficulty, and a very strong associated cycling culture. Some of the bike routes pass through remarkably wealthy and quaint communities, and also access tons of parks.
With or without a bike, I highly recommend all of the ferries across San Francisco Bay. The main ones that I've used frequently are the Sausalito, Larkspur, and Oakland/Alameda ferries. You get a beautiful view of the Bay while crossing. (Also Angel Island, only accessible by ferry, is a state park with great hiking or cycling around the elevated perimeter road, and an immigration museum.) The ferries are also great in combination with a bike ride; bike rental places will try to encourage you to ride across the Golden Gate Bridge and return via ferry. I just recommend against taking the Sausalito ferry southbound with a bicycle on a weekend, because it will be so packed with tourists that you might not even be able to get on.
If you're nostalgic or otherwise enthusiastic about classic video games, Alameda (an island suburb in the East Bay) has two establishments that preserve arcade games and pinball machines and make them available to play:
I don't remember everything that was suggested, but:
Exploratorium (San Francisco)
Lawrence Hall of Science (Berkeley Hills)
Chabot Space and Science Center (Oakland Hills)
Computer History Museum (Mountain View)
Maybe see if you can get a tour at Lawrence Berkeley Lab, SLAC (the Stanford accelerator), or NASA Ames Research Center? All of them have had tours on occasion but might not offer them regularly.
Silicon Valley used to have some very beloved electronics and surplus equipment stores, but I think most of them have closed permanently. :-(
Over on Green Street there's a plaque for the site where Philo T. Farnsworth invented television (!) but no other historic site to actually visit. This is quite nearby a pair of beautiful garden-lined walkways up to Coit Tower (the Greenwich Steps and the Filbert Steps) so you could see the plaque when planning to walk up there.
The Cable Car Museum is cool because you can see the wheels that are physically pulling the cables for the cable cars (right now, not just in the past).
