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Walk through the old town and admire the renaissance buildings.
Visit the Munot fortress and enjoy the view over the old city and the beautiful landscape.
The Rheinfall is the largest waterfall in Europe, served by two train stations: Schloss Laufen am Rheinfall (closed in winter) and Neuhausen Rheinfall (you can also use the Neuhausen Bad Bhf station, but it will require a short walk along the Rhine). The former station is more convenient for the main tourist route and all the observation platforms - it starts at the Laufen castle (Fr. 5 or €5, adults). The latter is better if you plan to take a tourist boat, and for a nice view over the castle and the waterfall together. There exist several boat routes - just to cross the Rhine near the waterfall (the cheapest option), to get very close to the waterfall and back, or to go to an outcropping in the middle of the falls (the most expensive option). A speciality is the firework on the night of the 1st August (national holiday).
Get in: From Zürich: take S-Bahn S16 towards Thayngen, get off not at Schaffhausen, but at Winterthur. Change for line S33 towards Schaffhausen, and get off at SLaR (during winter, get off at Dachsen and take bus 634 from there). From Schaffhausen, Take S-Bahn S33 two stops to 'Schloss Laufen am Rheinfall", or S-Bahn S22 two stops to 'Neuhausen Rheinfall' (Fr. 3.20) (or an Erzingen-bound local train one stop to Neuhausen Bad Bhf, and by foot from there).
If you're fond of long walking, you can also make the full way from Schaffhausen to the Rheinfall by foot, there is a nice walking road along the Rhine.
Museum telling much of the region's history.
Local playhouse with a beautiful interior decoration.