This is a massive museum. It is best, especially with kids, to pick a few exhibits to see and then leave. Most kids I have noticed love the Egypt section, the Medieval Knight area, and the Modern Art section. There is a kid-friendly cafe in the basement. A children's workshop room is being built at the basement-level entrance, which is the kid's entrance. There is a castle theme park across the street on 5th ave. You can even have an NYC bagel at Tal's Bagels on Lexington Ave or buy something at a food cart in Central Park.
The coat check is now open but only on the main floor. We always enter at the lower level kids entrance near 81st Street on 5th ave, as the lines are better and there is a washroom right there. We have a membership so we just go right in, we are allowed to bring guest.