Can I get a prescription from a doctor in New York City

Nope, but NY also offers medical, there are dispensaries in the city.

If you live in New York and have a license for medical marijuana, search for dispensaries in New York to fill your prescription. If you don't have a license, search for a doctor who can issue one. Each state has its own rules, at this stage, you can only purchase in New Jersey with a NJMMP license.

No has to be NJMMP

No their is no reciprocity as of yet.