There are a lot of decent public (state) schools outside of LA proper, Calabasas High where I went for a short while was very good, and the whole surrounds I've been told are pretty good too. The area is also pretty green as far as LA goes, particularly Thousand Oaks, Topanga Canyon, Woodland Hills etc and Malibu (coast) isn't very far. Nonetheless the area is very expensive, though maybe with the housing bubble burst property is more affordable. Personally, I found the area a pretty insipid, gentrified area, but I was also an angsty kid. I also don't know how the area would relate to your husband's professional requirements, but I'm guessing it would be too far. There are also a lot of good private schools closer to the metropolitan centre, even where not-so-great LA Unified schools prevail (and not every public school is bad).
Culver City is a great part of LA especially if you are on tight budget. Its very diverse and cosmopolitan - something you'll be used to as you are coming from London. The San Fernando Valley and Pasadena are very family friendly areas which are close to good schools. Take a look at the Expat Arrivals page on Areas and Suburbs of Los Angeles for more details.
LA has a great public transport network, so you'll find it easy to get about and commute to work.
Good luck with your move to the USA!