Yes, the hotels that are right on the beach do charge a premium. In that case, I would definitely stay in Santa Monica (NOT Venice Beach which is close by and great to visit in the day but not safe at night) as it's on the coast and the breeze will keep you a little cooler. Also, thereare some places to stay that have tiny kitchenettes which might be good if your lo doesn't always want to eat out. No matter where you stay you will need to hire a car as LA is a huge sprawl. From Santa Monica, the furthest trip you would likely have is over to Universal Studios, which probably takes about 45mins to an hour, depending on traffic. It's a good place to visit with littel ones, not neccessarily the theme park although I think that would be fun too as they have things for small folk, but there's a place in the complex called Universal City Walk which is like a funky shopping area with restaurants and fountains that kids can play in. It's a good place to go and just look and there are no cars so you know they will be safe.
Other places to visit: The La Brea Tar Pits - woolly mammoths and other ancient beasts that were pulled out of these still oozing tar beds right in the middle of the city.
J. Paul Getty Museum - you used to have to book this and I don't know about their kids policy, but I think they have opened a big new version now so might be more family friendly. Fantastic art collection.
If you can face the drive, The Huntingdon Library in Pasadena is gorgeous - the library itself has a lot to look at, but the grounds are amazing with different gardens and big lawns for running around safely. It's a real oasis when the city is steaming. Downtown Pasadena itself is lovely too, it looks more like we would expect a typical American town to look.
I'll keep thinking.