The Zwaanendael Museum is the obvious place to start in Lewes. Built in 1931 to mark the 300th anniversary of the Zwaanendael colony, the building is a 1:1 copy of the town hall in Hoorn, the Netherlands — gabled, red-brick, slightly too ornate for its surroundings, and entirely on purpose. The exhibits cover Lewes's Dutch founding, its maritime history, the 1813 British bombardment, and the local oddities that have washed up over four centuries on the bay.
The museum is free and small enough to see in an hour. Look for the Fiji merman in the curiosities case, and the cannonballs recovered from the town after the War of 1812. The staff are local and happy to explain why a Sussex County beach town has a Dutch town hall in the middle of it.