St John's Kirk is the oldest building in central Perth and the reason the city originally bore the name "St Johnstoun." The church was founded in the 12th century, substantially rebuilt in the 15th, and has been the scene of some of the most consequential events in Scottish religious history.
The kirk is free to enter and worth 30–45 minutes. The interior retains its medieval proportions despite significant 19th-century restoration, and the stained glass includes some excellent 20th-century work. The church is still an active parish, so check opening hours. It's in the centre of Perth's pedestrianised shopping area and easy to combine with the museum and the vennels.