According to New York's brochure for new drivers there are parts of New York in which you can drive alone when you have a junior license (not a junior permit) while there are still some areas of the state in which you cannot yet drive alone.
With a limited junior license you may not drive alone in New York City (the 5 boroughs) or in Long Island (Nassau and Suffolk counties) and Westchester, Rockland and Putnam.
Upstate New York and all other NYS counties not listed prior with a limited junior license your may drive alone, during the hours of 5 AM to 9 PM, for:
1. School course or activity
2. Employment
3. Medical appointment
4. Regularly-scheduled daycare for your child or a child of immediate family member
All other driving must be under the immediate supervision of a person who is at least age 21 and has a license valid for the vehicle being driven,
[Let CarInsurance.com help you find affordable auto insurance now.] For the hours from 9 PM to 5 AM you may drive alone for:
1. School course
2. Employment
3. Medical appointment
All other driving must be under the immediate supervision of your parent, guardian, person "in loco parentis," who is at least age 21 and has a license valid for the vehicle being driven.
For either set of hours you will need to have proper documentation so that you have proof that you are driving for employment, a medical appointment, etc. The NYS Department of Motor Vehicles can give you more information on what documentation is required if you need to drive with a limited junior license for one of these reasons.
With a full junior license you still are not allowed to drive in the 5 boroughs that make up New York City, In Long Island (Nassau & Suffolk) during the hours of 5 AM and 9 PM you may drive alone only directly between your home and employment, a work-study program, a course at a college, university, or registered evening high school, a driver education course, or while engaged in farm employment.
For this same area during the hours of 9 PM and 5 AM you may drive alone only directly between your home and a work-study program, a course at a college, university, or registered evening high school, a driver education course, or while engaged in farm employment.
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Upstate and all other counties of New York you may drive from 5 AM to 9 PM alone, so without being accompanied by a supervising adult. For the hours of 9 PM to 5 AM you may drive alone only when traveling directly between your home and employment or a school course. All other driving must be accompanied by your licensed parent, guardian, or person "in loco parentis."
If you are age 17, you are eligible for a senior driver license (Class D or M) if you have a junior driver license or limited junior driver license and have completed a state-approved high school or college driver education course. If you do not convert your junior license to a senior license, you are subject to the restrictions for junior drivers until you are age 18, even if you carry the completion certificate with you. | 
