One of the island's highlights, this evocative museum occupies an 1847 spermaceti (whale oil) candle factory and the excellent exhibits relive Nantucket's 19th-century heyday as the whaling center of the world. There's a worthwhile, albeit long (54 minutes), documentary on the island, incredible scrimshaw exhibits (engravings and carvings done by sailors on ivory, whalebone or baleen) and a 46ft sperm-whale skeleton rising above it all. Be sure to head to the rooftop deck for lovely views.
Admission is steep, but depending on which level you choose you'll have access to other sites around town. With the all-access pass you get admission to several preserved houses, which often function as their own small museums.