I put this day tour together using the excellent Swiss public transport network. It wasn't even necessary to go into Zurich in order to get started, as there is a regular service from Kloten to Winterthur, the connecting point for both Schaffhausen and Stein am Rhein.
Rhine Falls
The Rhine Falls near Schaffhausen form the largest waterfall in Europe, but it is a rather tame affair compared to the likes of Niagara, Iguassu or the Victoria Falls. This being Switzerland, it's possible to get off a train just a few steps from the falls and then continue your journey to Schaffhausen when you've seen enough.
Schaffhausen old town
Schaffhausen has a beautiful old town district featuring Renaissance buildings. It is towered over, quite literally, by the Munot fortress.
Stein am Rhein
Prior to doing research for this trip, I hadn't even heard of Stein am Rhein. This now seems odd, as it would be a credible contender for the title of prettiest village in Europe, and probably the world.
The boat trip from Schaffhausen to Stein am Rhein (and onwards to Kreuzlingen on Lake Constance) is reckoned to be one of the most attractive in Europe. Unfortunately, I was only able to experience it in part on this occasion: due to low waters, there was a replacement bus for the section Diessenhofen - Stein am Rhein.
Base: Hilton Zurich Airport
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