Around 5 hours drive from New York City I want to introduce you: Lake Placid
Frozen lakes, beautiful landscapes, tons of activities Here we go!
Whiteface mountain is the closest ski resort.
https://www.whiteface.com
There you can buy your tickets, rent your ski, book you ski lessons.
Whiteface Snow sports
You can drop off your kids there (starting at 1 years old)
For the oldest kids everything is organize, ski lessons by levels, lunch on site…
For the safety of your kids they give you a pager in case they need to contact you.
So you will feel free to enjoy your day with no worries.
Restaurants
Lots of grab and go, hot dog, soups and donuts and nothing on the slopes (Like in Europe)
Here in Lake placid you are here first of all to ski!
Village Of lake Placid-After ski
The village is just beautiful, you can have a tea time: Cupcake or a hot chocolate
On site there is also a huge ice skating rink and if you want to do a super family activity you can try the sledding tour.
Hotels
For a recommendation, I would say that the mirror lake resort is one of the best for families and it is very close to the european standard.
Note that there is no hotel on slopes, it will take you around 20 minutes with the hotel shuffle access the ski resort.
https://www.mirrorlakeinn.com
Enjoy your trip!