If OP is traveling in the first half of Feb they could find some good Hotel Week deals.

My family of four (two young kids also) have had relatively recent stays at the "value" options mentioned already: Gild Hall, HP LIC, and HR Jersey City. They all have drawbacks and they're all compromises (for the sake of value). Still depending on what the OP's needs and budget is, one of those could be a good option. However, whenever we return to NYC I'm definitely hoping to stay in a more central location even if it means spending a good bit more.