We love live music. Laid back loud family places. Boat tours are fun, too.
I'm not sure when you'll be here but if you're here any time from about the end of June to early fall, you should definitely check out the Hollywood Bowl. They have great programs for kids as well as sing-a-longs of movies like The Sound of Music. You can bring your own food and have a picnic beforehand. It's actually my most favorite thing to do in the city. I might also check out Descanso Gardens. Not only is it a lovely, laid back, fragrant place that is very kid friendly, they have a little choo-choo train that goes through the grounds. Don't know how old your children are, but they might love it. They often have live concerts there, too--the last time I was there they had a musician playing Japanese music during the cherry blossom festival. It couldn't have been more lovely.
I would check out LACMA or MOCA to see if they have any outdoor/free events when you're in town. There are TONS of opportunities (in parks, w/ movies, etc.) during the late spring/summer months, though since it's LA, others are year-round.
There used to be music every Friday night at The Getty Center - that might still be running.