Tryon Palace is the main reason New Bern is more than a pretty river stop. The original 1770 governor's residence burned in the late eighteenth century, but the reconstructed palace, gardens, and surrounding historic buildings make the colonial capital easy to picture.
The North Carolina History Center beside it broadens the story beyond the governor's house, with exhibits on the town's port trade, river life, and early North Carolina. If you only pay for one attraction in New Bern, make it this one.