Yes, there is a lighthouse on the Roanoke River in Plymouth. This is a somewhat recent addition to the town's historic past.
This is actually a replica of a lighthouse that used to be at the mouth of the Roanoke River, in the Albemarle Sound, more than a hundred years ago. Inside you will find artwork and history of the lighthouse, but you won't have to go in to find the cache. Please do not climb on the structure. If you'd like to look around please use the stairs. The lighthouse is open from Tuesdays through Saturdays from 11AM to 3PM but the cache is always available.
You should also visit the boat museum across the street (next to Beacon Printing) where you will find many wooden boats built and used in the Roanoke River and Albemarle Sound during the last century.
Please note that GSAK is wrong. While the river is inside Bertie County the lighthouse is in Washington County.