Many thanks to all those who gave ideas and tips for this visit. We successfully used the public transport ideas, walked our socks off and thoroughly enjoyed visiting many of the places mentioned. The weather was good too 
@4mummy Where is the original thread? We are going to be in LA for a few days and would be interested in what was suggested and what you ended up enjoying. My son lives there and we have been before, but always looking for new and interesting spots to check out. B-)
There were 2 threads on Parent Cafe. The one we used posted towards the end of last year but I am afraid that I gave up trying to find it, hence this thread.
As we had been to LA before about 10 years ago and visited Warner Bros Studios, the Getty museum, Santa Monica and Venice Beach and the Hollywood Boulevard and Walk of Fame then, we concentrated on places new to us. This time we included Griffiths Observatory, La Brea Tar pits, the Walt Disney concert hall designed by Gehry, Olvera Street and the oldest house, and the Cathedral of our Lady of the Angels Catholic Church with it beautiful plaza of fountains and sculpture. We ate lunch in the Grand Central market and basically meandered around those areas and found ourselves briefly in China Town at one point as well. We would have liked to visit at least one of the art galleries recommended but time was against us. We did not attempt any of the shopping areas and decided against organised walks in favour of longer at fewer places. Sadly we did not have enough time to explore Griffiths Park, which looked very tempting or to visit Manhatten Beach.
We stayed near LAX, used the shuttle to the airport and the Flyaway bus to Union Station. From there we walked in the downtown area or caught the metro to other places. We visited the Observatory on a Saturday, when there is a link bus for the final stretch.
There were many other excellent suggestions, so good luck with your thread search.
We recently visited the Tar Pits also; I found them fascinating. Never knew that camels once lived in that part of the US!