The fastest route from Syracuse to Charlotte (in Chautauqua County, western New York) is via Interstate 81 South to I-90 West (NY Thruway) to I-86 West, taking approximately 5 hours 30 minutes (about 330 miles) without traffic.
Alternative routes using NY-20 West or NY-155 South add roughly an hour. Actual travel time varies with traffic, weather, and Thruway conditions.
Note: Ensure you mean Charlotte, NY (near Buffalo), not Charlotte, NC (which is ~700 miles, 11+ hours).