funny thing... reading your question kept thinking oh perfect place would be mystic...!!!
so spent some considerable time thinking looking and here is what I found could be the right one
http://www.tripadvisor.com/Travel-g40790...
the tripadvisor.com is the MOST fabulous place to find things where to stay what to day where to eat how to get there etc etc so hope that idea helps oh and not sure about the 4 hrs thing...
seems to get really good reviews family friendly and there may not be trains BUT there are trolley cars
Edit... well I was pretty spot on for distance just googled it is 4 hrs 35 mins driving time from NYC
There are some places for a family vacation....
1.New York City, New York, United States
New York's many zoos, museums and landmarks make the city a perfect destination for families of all ages. Explore Times Square or take the kids to FAO Schwarz, take a boat ride to the Statue of Liberty or an elevator to the top of the Empire State Building, eat lunch at Carnegie Deli or picnic in Central Park - the choices are endless.
2.Paris, Ile-de-France, France
The City of Lights shines bright for kids of all ages. Living up to every pre-trip fantasy, Paris has a constellation of starring sights from the atmospheric Notre Dame to the elegant Eiffel Tower to thrilling Parc Asterix, DisneyLand Paris and the wonders of the Louvre. Prepare to be dazzled.
3.Playa del Carmen, Yucatan Peninsula, Mexico
Playa del Carmen, on the Mexican Caribbean, is home to sandy beaches, Mayan archaeological sites and child-centered theme parks. Kids and adults enjoy clambering through Discovery Jungle Park's authentic rope bridges and exploring Xcaret's underground rivers, butterfly pavilion and aquarium.
4.London, England, United Kingdom
Offering the irresistible combination of atmosphere, history and the thrills of a vast, fast-paced city, London makes a majestic destination. From the ghoulish Tower of London and the pomp of Buckingham Palace to the buzz of a big wheel, the London Eye, this is a city that will have you in a spin.
5.Cancun, Yucatan Peninsula, Mexico
Cancun is one of Mexico's most famous destinations, and despite its reputation as a spring-break paradise, families will find plenty to do here, too. Explore ancient Mayan ruins, the Xel-Ha waterpark and the thrilling Interactive Aquarium, or just enjoy beautiful beaches.
I think Venice is the perfect place for family vacation. There are so many famous places like St Mark's Basilica,the Grand Canal,the Piazza San Marco,the Lido di Venezia, San Clemente Palace Hotel and Resort etc.
no idea sorrry...just my points anyways and hope you find one