Kazunori is a great choice, but no sushi, just great hand rolls.
Hide Sushi on Sawtelle is good - not great - with a nice price point.
Sasubune on Wilshire in West LA is pricier and better quality.
I have been disappointed in Kiriko lately, but most around here think it is still good.
Hamasaku on Santa Monica Blvd is know for “krazy” roll combos but also has pretty good straight sushi - might be perfect with kids.
If the kids, and you, are in for the best quality, lots of fish flown from Japan, the best places are Shunji, Mori, and Tsujita Sushi. And both Shunji and Tsujita Sushi have very reasonable lunch specials.
Wadatsumi on Pico has good sushi - limited selection - as well as lots of other Izakaya options done well. And Westside Tavern next door has great beer. COLDEST beer in town, I think.