For people like me who need to escape from the City once in a while, here is a cheap and easy option for a day trip:
Cold Spring, NY
Easy, peezee : choose a sunny day, get to Grand Central, take a round-trip to Cold Spring (less that $20), hop on the Metro North and sit on the left side to enjoy the nice view during the ride.
Once in Cold Spring, explore, follow your intuition. Bunch of restaurants on main Street will delight your palate. I have no specific recommandations, just listen to your taste.
The only thing I would recommend is this little trail by the river off the road 9d.
On Main St, take a left on Fair St, go all the way until the forest, the trail starts here : Stony Point Park and you can swim! Yeah, not so sure if it's clean but oh well, it won't hurt for one day...
Don't forget to bring something to grill and have fun!