Pärnu Museum is the city's best indoor introduction, especially if you arrive outside beach season. The exhibits cover the region from Stone Age finds through Hanseatic trade, Swedish and Russian rule, resort life, and twentieth-century upheaval.
It is not a huge museum, but it gives the city useful depth. After an hour here, Tallinn Gate, the Red Tower, and the spa buildings stop feeling like isolated sights and start to read as pieces of one coastal town with several lives.