If you are properly licensed, I am inclined to say yes (crossing the border alone may be an issue...).
The page http://www.nydmv.state.ny.us/license.htm… says:
"You must have a NYS driver license or a valid driver license from another US state or from Canada to drive in NYS. In most cases, you can drive in NYS if you have a valid driver license from another country. See "Drivers From Other Nations". The minimum driving age in NYS is 16."
Then it says:
"NYS restricts driving privileges if:
* you are under the age of 18 and have an out-of-state driver license, or
* you are any age and you have an out-of-state learner permit."
So basically, because you're under 18, you'll need to follow the restrictions listed here in the "upstate" region (even though Buffalo is obviously Western NY): http://www.nydmv.state.ny.us/youngerdriv… Basically, you may drive alone from 5AM-9PM with up to two non-family members under 21. No use of electronic devices is permitted.
Your G2 license allows you to drive without supervision. So in terms of being properly licensed, you are good to go as long as you meet all the current restrictions of your G2 license. Whether a minor can cross the border unaccompanied without prior arrangements is another matter entirely.
Buffalo NY? Unfortunatly NY Law states a driver with a JUnior license or permit is not able to drive in the vehicle without a licensed driver over the age of 21. If you did get pulled over they will either impound your car and take you to the police station and/or write you tickets and suspend your license. I dont reccomdend doing this.