The dot lies a few kilometres south of the Rhine in the quiet Unterland of Zurich canton, near the villages of Rorbas and Freienstein, where the Töss river flows through orchards and woods before it meets the larger river. Schaffhausen itself is further north, but this is the stretch of country that leads you to it, with modest farms, half-timbered houses and the Rhine's wide green valley just beyond the ridge.
When you do reach Schaffhausen, the town is a treat. The old centre is one of the best preserved in Switzerland, with painted facades, bay windows called Erker, and a hilltop fortress named the Munot, built in the sixteenth century as a circular citadel, where a watchman still lives and a bell rings in the evening. A short distance downstream from the old town, the Rhine Falls drop about twenty-three metres over a width of about a hundred and fifty, the largest plain waterfall in Europe. Boats take visitors to a rock in the middle of the thundering water, and the spray makes the air feel cold even in July.
The Grand Tour of Switzerland is a route of some 1,600 kilometres that links the country's best-known sights, created in the 2010s as a tourism product, and it works well as a way to see the variety of the landscape, from lakes to glaciers. For a rider, the Swiss rules are strict, and speed cameras are widespread, with heavy fines that scale to income. A motorway vignette is required for the motorway network, and the standard speed limits are 120 on the motorway, 80 outside towns and 50 inside. Obeying them is half of enjoying the country.
The riding here is gentle, with modest hills, smooth tarmac and very little to alarm you. Traffic around Zurich and the airport can be heavy at rush hour. Eglisau, a pretty walled town on the Rhine just to the north, has an old bridge and a view of the river from the terraces of its cafes.
Fuel and food are easy in the villages and towns, though prices are high by European standards. Many riders fill up just across the German border if the route allows.