I wouldn't recommend staying in Los Angeles. It's not necessary and there's few nice places to stay in the city.
Santa Monica is a wonderful place to stay with lots to see in that area. It's a good 30 min drive from Hollywood/Beverly Hills at most times of the day though.
If you wanted to be closer, there's the Beverly Hilton hotel. It's a pretty standard Hilton and a little overpriced but the location is fabulous. It's walking distance to Rodeo Drive (well, a few blocks) and although it's on the crossways of two major roads, the surrounding areas are really pretty and make for a nice evening stroll. Plus, as a perk, every time I've stayed there I've seen LOADS of celebrities going to the numerous nightly events they have at the ballroom there (it's where they have the Golden Globes). The kids might get a kick out that.
Another alternative, since you're going to WB, is to stay in Burbank. We stayed at a really beautiful hotel there called the Graciela. It was pretty expensive though but definitely worth it. More like a boutique hotel, it had the best beds I've ever stayed at hands down and was close to Universal and WB as well as only a short trip down the hill into Hollywood etc.
If you've got the time, and the kids are into space at all, I'd really recommend a visit to the Griffith Park Observatory. It's in the Hollywood hills and has the best views of the Hollywood sign and the whole of LA. There's all kinds of interesting space exhibits and a really good (and reasonably priced) planetarium show. They've just remodeled it and it has a really nice new cafe there.