I live near the museum, so I can't really comment, but your itinerary coming from LA would look one three ways:
1) Straight day trip - doable, but not my favorite
You would book a flight early morning from LAX/BUR/LGB/SNA to SFO/OAK (any combination that fits your budget and schedule). It would have to be Thursday-Sunday as the museum is
closed Monday-Wednesday.
I would land no later than 9am, eat your breakfast in So-Cal/at the airport or take it on the plane. Officially, it is 35 minutes from SFO to the museum, but allot 1 hour. Take an Uber directly from SFO (rental car not recommended for such a short trip). From OAK, it is 45 minutes,
but you would hit AM commute traffic on Thursday or Friday that funnels onto a 5 lane bridge, would not advise.
Museum opens at 10am, make sure you have correctly timed tickets. I'm thinking one can spend 3-4 hours at the museum, or more, it's
super dense. Not really small kid friendly.
At this point, up to you what to do -- head straight back to the airport, fly to LA/Orange County, and have dinner? Head into SF itself and grab dinner, then take the last flight out? I would probably not leave the confines of the peninsula (the strip of land from SFO to the south, to the Golden Gate Bridge to the north). If you have time, you can consider flying out of OAK if it better serves your budget.
If it were me, I would take an Uber to the
Ferry Building down by the Bay Bridge, and have a late lunch/early dinner at
Hog Island (recommend the clam chowder), or
Gott's if you're in a burger mood (might I recommend the kimchi burger with gochujang mayo). Once you're done, you can take an Uber back to SFO, or you can actually hop on BART (Embarcadero Station) which takes you right into the terminals at SFO (or OAK via connector train).
I'm pulling random Thursdays in February and you're probably looking at $95-$200 RT per person for airfare, which will be the bulk of cost here. Example: February 22, 2024 on Southwest Airlines I see a $46 fare from LAX to SFO that lands at 7:40am (you'll have time for breakfast somewhere!), and $49 from OAK to LGB on the last flight out. You will spend most of your planning figuring out the flights, because the costs are all over the place because you have compare 6 different airports and their pairings.
2) Overnight
I would use the above template, but instead of heading back to the airport from the Ferry Building, you can probably do one of two things:
(a) Head to Napa Valley -- this is a popular getaway from SF and not too far (maybe an hour ish). Bring a nice outfit and shoes, dine at Thomas Keller's restaurants, drink the finest wine outside of France, etc...
(b) Stay in SF -- depending on the season, catch a baseball game at Oracle Park, go do touristy things, etc...
If you head to Napa, consider renting a car at the airport when you land and drive yourself to the Disney Family Museum, then you can jump off straight to Napa after you are done with the museum (take the Golden Gate Bridge, stop at the parking lots and enjoy the views). Make sure you don't leave valuables in the car and get the maximum car insurance possible, bipping is a thing, and your California Permanent Fleet sticker will be a dead giveaway you are a tourist in a rental.
If you stay in SF, just stick to Uber.
3) Full Weekend
I kind of ran out of steam with writing and have some work meetings, but I trust the rest of the board to chime in with weekend itineraries. You can even probably drive up to SF!