Jamestown, NY to New York University buses and trains from $69

Or, see buses and trains from New York University to Jamestown, NY.
Here are some trips other travelers have found on Routefriend.
13h 10m
2 stops
Amtrak Greyhound
13h 15m
1 stop
16h 49m
3 stops
Amtrak CoachUSA
15h 16m
2 stops
Amtrak Metro-North