Punane Torn (Red Tower) (located at Hommiku 18), which actually is white nowadays dates to the 15th century, which means that the building is the oldest one in Pärnu. Up there is a souvenir shop.
There's at least a couple of interesting art galleries. One of them is Chaplin Centre, Pärnu New Art Centre (Esplanaadi 10) – notice the hilarious headless and armless Lenin stature, with a blinking light as a 'head', in front of the gallery.
Another gallery worth visiting is Linnagalerii (City Gallery), at Ruutli 30. The entrance is free.