I lived there 30 years ago. Don't buy electronics in times sqare. I saw them selling PanasOanic radio's. I imagine it's now cell phones that are from Appel or something. Don't get snagged by a street hustlers card games. Be judicious about eating street food. Eat NY pizza. God I miss that!
See if your favorite authors lived there. I went to see where Louisa May Alcott lived and her neighborhood. shop at the street art/food/flea markets. Buy a small piece of art from a street vendor that created it. Have a handful of quarters or tokens for street performers. Play checkers with an old guy in the park. Be open to conversation. People do talk, don't be afraid-or weird. Eat a lot. Go to a Greek diner. I don't know why, but I liked them. Get out of Manhattan and visit queens or Brooklyn or my old neighborhood, gun hill road, in the Bronx. By the medical school or hospital.
Beautiful time to visit! Have a wonderful visit. Just experience the city.