The Alexander Hamilton Birthplace in Charlestown is the island's most internationally famous historical connection — this is where the first US Secretary of the Treasury and subject of a celebrated Broadway musical was born in 1755. The original house was destroyed by an earthquake, and what stands now is a reconstruction from the 1980s. It shares the site with the Museum of Nevis History, which contains more informative exhibits on the island's broader past: Amerindian occupation, the sugar plantation era, and the development of post-independence Nevis.
The Hamilton exhibits document his Nevisian childhood and trace his extraordinary later career in America. The museum is small and can be done in under an hour. It's in the centre of Charlestown near the courthouse, making it easy to combine with a walk around the town's Georgian-era waterfront buildings. Opening hours are typically weekday mornings; check in advance as hours can be irregular.