NBWM is absolutely fantastic. They have Clifford Ashley's (wrote Ashley Book of Knots) rope and knot collection, and some of his paintings too (he lived on the other side of the harbour). They also have the world's largest scrimshaw collection, and the Lagoda, the world's largest model wooden ship (1:2 scale IIRC), which you can walk around on and check out the ropework. Seamen's Bethel from Moby Dick is literally a block away. Easily the coolest museum I've been to.
Interesting bit of trivia, New Bedford used to be the richest city in the planet because of the whaling industry.
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