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The closest City to the Canadian Border from your location would be Kingston.
This depends also on what roads you would like to travel.
The travel distance is a little over 370 miles.
Here is the directions:https://maps.google.com/maps?q=map+of+new+york&ie=UTF-8&hq=&hnear=0x89c24fa5d33f083b:0xc80b8f06e177fe62,New+York,+NY&gl=us&ei=eXtTUuvgCtjd4AP8poCgBw&sqi=2&ved=0CCoQ8gEwAA
if you want to go sight seeing, I would suggest Niagara Falls!
I hope this is helpful. If you have more follow up questions please let me know. It is never a problem. I will go above and beyond to make sure you are 100% satisfied!