No real info, but two suggestions to throw out.
1. Newport, RI
2. Mystic, CT (I’ve heard there are attractions there. Dont really remember what exactly right now) I searched on mapquest NY, NY to Mystic, CT and it turned up as 2 hrs, 45 minutes. (not really sure how reliable the timing is, you would probably know better than me)
A few minutes invested in calling different hotels and getting some basic info which usually they wont mind sharing with you (if you’re a group, ask if theres any place in the are that will give you a better rate) and about local entertainment. Ask about state parks, where you can rent a boat, (have a picnic lunch?) which are have a family friendly budget.