Well, the counselor’s letter is really important. It gives more than a recommendation of you. It provides information about your HS, gives contexts for your grades, etc. Why would your counselor not supply this for you?
The counselor recommendation becomes available to the person who submits the school report in the Common Application after the school report is submitted. If you don’t have a GC at your school (like some international students don’t), then someone like the principal or a school administrator usually does it, I think. This might help you understand it better:
Most schools require a guidance counselor recommendation. Look at the requirements of each school online. If you don’t have a guidance counselor talk to a dean or principal at your school and ask him/her to write one.
In another post you say you have a 3.3 GPA and a 1410 SAT which makes all of these schools huge reaches. Also NYU is typically not very generous with financial aid if that is an issue. Be sure to create an application list that also has match and safety schools that appear affordable (run net price calculators) and that you would be happy to attend.