I love sitting outside at Cafe Claude - the food is well-prepared, well-presented traditional French fare - kiddos will love their chicken, fries, and yummy Croque Monsieur, and it's tucked down Claude Lane away from the Union Square tourist traps.
I used to work for Kimpton, so I'm a little biased, but P&P has a great kids program, and pretty darn fine tasty food, too. http://www.pucciniandpinetti.com/about_kids.php - Plus, they take reservations, so you can grab a last-minute reservation online on your phone and jump the line (disclaimer: OpenTable is also a former employer).
Nordstrom Bistro on their top floor is also a good bet, with a great view and much calmer vibe than the Westfield hordes down below. Disclaimer: I worked inventory at Nordstrom once in high school, so I may also be biased :)
Unfortunately I am not the best source for kid-friendly spots, and most of the ones I can think of are pretty tourist-trappy in Union Square... The best option I can think of is Pearl's for their awesome burgers, and they're only two blocks off Union Square.
Personally, I put up with the crowds and eat at Out the Door in the Westfield Centre. I did take a little one to Sears Fine Foods for their 18 mini pancakes, and they were thrilled.