Cold Spring, NY: Hike a 1400-ft. summit, one hour from NYC
Don't let the fact that Bull Hill is right next to Breakneck Ridge put you off.
Both have them have more to do with a particular bull they share in local lore than any threat to your well being. In fact, if you head north out of New York City for about an hour to Cold Spring (accessible by commuter rail MetroNorth, too), a hike up this 1400 foot mountain (it's also known as Mt. Taurus) will be salutary for your mind and body, we promise.
What's so appealing about Bull Hill is that there are several trails to the summit and while they're not suitable for novices, they're manageable for most with a few steep spots. On your way up, you'll pass the remains of the estate owned by Edward Cornish—dilapidated stone buildings that must have made up a beautiful property when it was occupied from the 1920s-1940s.
Best of all, when you get to the summit, you'll be rewarded with views of the gorgeous, pristine Hudson Valley and yes, if you look south you can even see NYC in the distance.
As for the bull, the local story is that a bull wandered off and up Breakneck Ridge and took a fatal fall. You're sure to have a better time.