The calculated distance (air line) between Traben-Trarbach and Nürnberg is approximately 180 miles respectively 290 kilometers.
By car or train, the actual journey to Nürnberg is certainly longer, as only the direct route (as the crow flies) between Traben-Trarbach and Nürnberg has been calculated here.
Air line (approximately)
290 kilometers
157 nautical miles