Also live in NYC - our teens like iced coffee from Blue Bottle and Birch (Birch has student discount), but it’s very expensive so only on special occasions. They usually get lemonade or bubble tea when they go to Koreatown. Our kids don’t like Starbucks - my work colleagues bought my kids a Starbucks gift card a year ago, but the girls still haven’t used it.
Our kids do make themselves coffee every morning to take to school. Some concoction where they mix Douwe Egberts Pure Gold freeze dried coffee (1/2 of a packet) with a tiny bit of hot water and then fill it to the top with milk.
Many of our kid’s friends are from East Asia, and the girls drink tea not coffee, and bring tea to school in their water bottles.