I love to people watch at Battery Park. There is a trail that goes along the water, and is rarely crowded. I second the Shake Shack recommendation, especially the Madison Square Park location. If you have a sweet tooth I recommend the carrot cake at Amy’s Bread. It is the best in the city. If doughnuts are your thing Doughnut Plant has great variety and my favorite is tres leche cake doughnut.
People watching, the 14th Street A/C/E during rush hour always has full on bands playing. Sometimes string quartets are playing upbeat tunes and selling their cd’s, there’s always someone playing horns downstairs. A lot of those busy subway stations–Union Square, too–are pretty awesome to be in during rush hour if you *aren’t* the one in a rush.
I always recommend the High Line, because even though it’s a tourist trap, it’s always changing. The art and pop up overpriced coffee shops and sounds and plant-life…I think it’s always a good spot. Enjoy!