The Museum of New Art is Pärnu's main contemporary art stop, with changing exhibitions that can be uneven but are rarely dull. It has an independent, slightly improvised feel that suits the city better than a polished white-cube gallery would.
Check the current programme before making a special detour. When the exhibition is strong, it gives Pärnu a cultural edge beyond spas and beach walks; when it is not, the visit is still short enough not to hurt.