I just came back from NY actually. Brooklyn Botanic Gardens is free admissions right now during the fall/winter months. Nothing too shady during the day, walked back from there through the brooklyn bridge to times square.
Want good chinese eats? Go to downtown Flushing for chinatown 2
Red Bowl Noodle Shop - Downtown Flushing - Flushing, NY went here and their braised beef noodle was damn good and it was under 10 bucks. I also found some bonus chicken. So bonus. They also have an all you can eat breakfast menu around 8 bucks.
Harlem is scary at night after a visit to a nearby museum to get to the station on 110 ave. Get yourself a bag of honey roasted peanuts. that shit is off the wall.