The HMS Trincomalee is the headline reason to come to Hartlepool. Launched in 1817 in Bombay, she is the oldest British warship still afloat — older than the USS Constitution by some measures, if you count which ship has stayed in the water longest. The teak hull is the original; the rigging and most of the deck fittings are exact recreations.
You can walk every deck from the captain's cabin down to the orlop deck below the waterline, with displays showing what life was like for the 240-odd crew. Combined ticket gets you the National Museum of the Royal Navy next door. Allow two hours for the ship alone.