This is a tough one. We lived in L.A. for 13 years and the things you want to see are often very far apart. I would recommend picking some favorites. LaBrea Tar Pits and the county art museum are fairly close together, with decent parking. Or Huntington Gardens in Pasadena has a range of different types of gardens, plus small, but good, art museum, a true British tea house (you do need advance reservations for that...it is very popular). And it is all in one spot, with a huge parking lot. Actually, this is the one I would recommend. It is beautiful architecture as well.
You would need to rent a car, though. While San Pedro is fun, most of the type of things you expressed an interest in are not near there.
Hope you find what you want!