With 2-3 nights I’d choose between San Diego or LA, maybe Santa Barbara.
In LA, Beverly Grove is a great area to stay. Park Plaza Lodge, Beverly Laurel Motor Hotel and Palihouse are all great options depending on your budget. In the area you have the La Brea Tarpits, Original Farmers Market, The Grove and Beverly Center (shopping), Academy Museum of Motion Pictures, Petersen Automotive Museum (movie and race cars) and what’s left of the LA Museum of Contemporary Art. It’s also a very family friendly, walkable neighbourhood with plenty of dining options mainly along West 3rd St. If you have time after all that, Griffith Park is excellent for kids with walks, Wild West museums, train rides, the Observatory and Zoo. Gets packed on weekends so try to visit on a weekday, you can easily spend all day there. A drive through Hollywood on the way there is all you need for that district.
I’ll leave SD and Santa Barbara to others to discuss. I’d also combine a SeKi trip with Monterey, Big Sur and Yosemite in the future over 10-12 days or so. The key with Yosemite particularly is booking well in advance (10-12 months) and staying in the Valley or National Park, not an hour or 2 away to save a few bucks.