A friend of mine, Richard Rosenblatt, has published a list at that link on city search which details his fav spots for the Los Angeles part of your journey.
For the family:
Will Rogers State Historic Park
1501 Will Rogers State Park Rd, Pacific Plsds, CA
"Amazing place to let the kids run free--you just can't believe that you are smack in the middle of Los Angeles and not in the middle of Idaho. On the weekends, kids can help wash and pet the horses; it is a lot of fun."
For the Parents:
AIR CONDITIONED
2819 Pico Blvd, Santa Monica, CA
"I am an owner in this bar because I love wine, and we worked hard to create a classy atmosphere, but with a fun element to encourage folks to try different wines. There are no snobs there, just a well-educated team that can guide you on a tour of the senses."