Going on a trip with small kids is always an expedition no matter what, but it all depends on your preference of course and when you have vacation. But besides this, if you’re visiting New York with kids, I think the best time would be during the spring or fall, when the weather is more comfortable.
April can be a bit cold if you’re unlucky, May is nice with all the trees and flowers blooming, and June is warm with little risk of rain. September and October is nice and cooler again after the summer, but not so rainy and cold as November can be.
During this period it’s is a bit less people as well, which fits a family with small kids perfect.
No parents enjoy a vacation with cranky kids because they are too hot or too cold, so this time of the year you can do outdoor activities and sightseeing.
You don’t need to bother with going up and down in the subway, and be totally sweaty of this expedition. Bring comfy shoes and plan ahead, bring a stroller for the smaller kids, pack snacks and take a break in one of many parks along your walks in Manhattan.