St John's House is a handsome Jacobean mansion just east of the town centre. It was built around 1626 on the site of a medieval hospital. The interior is now divided between a museum of Warwickshire social history and the regimental museum of the Royal Warwickshire Regiment — both small, well-presented, and free.
Outside there is a Victorian schoolroom restored to look as it would have done in 1880, and a re-created Victorian parlour. Worth an hour if you have time after the castle. Closed Mondays.