Congrats! You’re going to do just fine, and trust me, you will grow so much from this trip. I have stuttered my whole life and in December of 2017 I traveled to Taiwan for 4 weeks totally alone. It was by far one of the best experiences of my life. New York is just the first step for you, once you feel comfortable with this you’ll realize that your stutter will only hold you back if you allow it to. Have fun!