Here's a suggestion for Syracuse: Dinosaur Barbeque. This place is as genuine as BBQ gets in New York - people travel for hours to tuck into a plate of ribs. Great live music, fun, casual & not too expensive. Don't be put off by the staff - they can be a little abrupt, it's part of the charm! The restaurant is on Willow Street in Syracuse, and I think they have a web site.
Enjoy your trip to New York State
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