To have the best lunches like a 'fried peanut butter sandwich', lounge or book a room for a few days in the heart of the city, visit 'The Ace Hotel'. Ease down in the couches, order a Brooklyn Beer and relax. A great place to meet up.
You can't say you've seen NYC until you've seen it from a boat. Hop on the ferry from anywhere to anywhere and you'll see what I mean. Not only will you see excellent old buildings and factories--the inner workings of the old industrial city--but you'll head out under working bridges and see the skyscrapers in all their towering glory. And once you've done it, do it again, at night.
My second-favorite outdoor-place in Manhattan. The abandoned 1.6 km rail tracks running above Chelsea down to the Meatpacking district were turned into an above-ground park. Perfectly nice place for sitting in the sun, reading, relaxing, having lunch in some green spot in the city. Nice views at the Hudson River, New Jersey, the Statue of Liberty (little small from there but still visible) and the architecture around Chelsea.