Spring and early summer are the best time to visit Schaffhausen. The Rhine Falls reach their maximum volume in May and June when Alpine snowmelt peaks — the difference between a June visit and a September visit is substantial. By late summer the flow drops and the falls, while still impressive, lose some of their force.
Summer brings crowds to the Rhine Falls but the old town itself stays manageable. Autumn is good for walking the Altstadt when the light is lower and the tourist pressure has eased. Winter is cold and quiet, but the Schaffhausen Christmas market is a proper local event rather than a purely commercial affair, and the Munot and old town look well in frost. The Museum zu Allerheiligen is a year-round draw.