The state puppet museum has lots of historic puppets behind glass but plenty to play with too. There's a Cellar of Horrors full of 'evil and scary puppets' (including a vampiric rabbit), a dress-up room, a shadow theatre and windows into the workshops where the puppets are made. Sadly there aren't any puppet shows in summer, but on the weekends at other times they're included in the price. Performances are in Estonian, but the visual fun is multilingual.
