Monmouth Castle is fragmentary now, but it still matters: Henry V was born here in 1386, and the surviving ruins sit beside Great Castle House. The small volunteer-run museum tells the story of the Royal Monmouthshire Royal Engineers, a militia regiment whose roots reach back to a 1539 muster.
It is not a blockbuster museum, but it gives useful depth to a town that can otherwise look like a simple market stop. Check current opening before making it the centre of a visit.