Governor's Island in the East River, just 1 km from Manhattan, is an oasis away from the hustle and bustle of the city. Catch the free ferry from downtown near Battery Park and enjoy gorgeous views of the city, car-free bike roads, picnics and free entertainment such as concerts and art exhibits. Fun for all ages. There are many available food options on the island or, you can pack a picnic lunch. There is, appropriately titled, an actual picnic point.
If you're lucky enough to snag a ticket, one of the finest ways to leave Manhattan for Governor's Island is also to escape to the early 20th century. Each summer during two weekends, the Jazz Age Lawn Party brings 1920's music, cars, and attire to the London Plane-shaded lawn at Colonel's Row.