According to the New York Department of Motor Vehicles, no matter what age you are, if you hold a learner permit, you may not drive:

• Unless accompanied by a supervising driver at least age 21 who has a license valid for operating the type of vehicle you are driving. For example, only a person with a motorcycle license may supervise a motorcycle learner.
• In a DMV road test area.
• On any street within a park in New York City, or any bridge or tunnel under the jurisdiction of the Triborough Bridge and Tunnel Authority.
• On the Cross County, Hutchinson River, Saw Mill River, or Taconic State parkways in Westchester County.

Once you move up from a learner's license and obtain a junior learner permit or junior driver’s license you have restrictions which include:

• You may not drive with more than two passengers under the age of 21 unless they are members of your immediate family, or your accompanying driver is your licensed parent, guardian, person "in loco parentis," driver education teacher or driving school instructor.
• You and each passenger must wear a seat belt.
• The only passenger allowed in the front seat is your accompanying driver.

There are also regional restrictions for those with a junior permit. You mentioned you live in New York City so the conditions for this are of NYS include:

From 5 am to 9 pm you must drive only under the immediate supervision of your:
1. Parent
2. Guardian
3. Person "in loco parentis"
4. Driver Education Teacher
5. Driving School Instructor

The person above must be at least age 21 and have a license valid for the vehicle being driven.

Vehicle must have dual controls (dual brakes)

From the hours of 9 pm to 5 am you must NOT drive as a restriction of a junior license for the NYC area (5 Boroughs). There are also restrictions for Long Island and Upstate New York with a junior license.

As for your question, from this information we obtained from the New York State DMV it does not appear that you can drive with a learner's permit at any time without a supervising licensed driver who is at least age 21 years of age in the car with you.

To read more about the conditions placed on the various permits and licenses that are part of the graduated drivers licensing process in New York State and also the regional restricted, contact the NYS DMV. You can also check out this NYS DMV brochure for new drivers.