We spent about a fortnight in SF last Easter and it was wonderful. My favourite part is the beach - so endless, it's my fantasy now to live in a big city and in the evening walk the dog on the beach.
No car but we stayed fairly centrally, in Outer Richmond (12 min walk to the Golden Gate park), Uber fairly cheap and a reasonable bus service.
Pier 39 is indeed tickbox SF but too touristy so we didn't bother this time. Exploratorium was amazing, make sure you arrive early as it's a full day experience. Morrison Planetarium is mind-boggling, the largest digital dome in the world. It is part of the California Academy of Science Museum in the Golden Gate Park which also houses an aquarium, a rainforest experience and a natural history museum - think the London Science Museum + Natural History Museum on steroids. Again, at least a day or 2 half-days (I think the tickets are valid for three days). De Young Museum (art; the oldest museum in SF) is in the Golden Gate Park too as well as the Japanese garden.
Walk in Sutro Heights and the Land's end trail with a stroll down El Carmino del Mar with tech bros' mansions against the backdrop of fabulous sunsets.
If you have a car, you might enjoy spending a few days in Napa and Sonoma getting slightly sozzled in the vineyards. Th Redwood National Park with sequoia trees is majestic, it is one place we always go to when in CA. Carmel is lovely but a bit too perfect, all galleries and chichi shops, like a Californian version of Notting Hill. Monterey has one of the best aquariums.
There are some very dark sides in SF as well, every time we come there are more and more homeless people; we had a terrifying moment on the bus when a clearly stoned individual expressed aggression to a fellow passenger and everyone just averted their eyes (in bright daylight on Saturday). And an unexpected encounter with a naked man in cowboy boots drinking kombucha with his (dressed) mates in a public square in the financial district...