The train route to Syracuse from New York City travels considerably farther than the highway network does, as it follows the Hudson River north to Albany before turning west. As such, even under optimal Amtrak operations, a rail trip will take longer than a road trip, whether in a car or bus. Moreover, the Empire Service runs only once daily, so if you miss your connection in New York, you are out of luck.
You didn't specify how flexible your travel dates were, but at this writing, round-trip midweek nonstop flights in January 2017 are showing on Kayak for $117 (JFK-SYR on jetBlue) and $127 (LGA-SYR on Delta Connection and EWR-SYR on United Express). Flight time is under 90 minutes for any of these options.
Of course, you must factor in an hour or two for security screening, and particularly for LGA or JFK, there will be significant extra time or expense required for a ground transfer from New York Penn Station. But if time is of the essence, NJ Transit to EWR isn't a terrible option (except for flying Commutair of course).