New York is one of the most densely populated cities in the United States. There’s a lot to love about it, but if you ask its residents, they’ll likely say it can feel too crowded, too dirty, and too chaotic. So it helps to have a place to escape to , if you can afford it.  North of the city, the Hudson Valley and the Catskills are home to many Gilded Age and early 1900s-era estates, from the Vanderbilt Mansion in  Hyde Park  to lavish  properties in Tuxedo Park . To the east, the Hamptons, on