Schaffhausen is the little Swiss city that wanders north of the Rhine, in a canton that pokes into Germany like a thumb, and from the border post you can hear the language change within a few kilometres. At about four hundred metres it is low country, with gentle hills, vineyards, and fields rolling towards the Black Forest.
The old town is one of the best preserved in Switzerland, with rows of medieval houses carrying painted facades and elaborate oriel windows, the Erker, that stick out from the upper floors like glassed-in balconies. Above it, the round fortress of the Munot dominates the hill, a sixteenth-century circular bastion that you can walk right around, and the view over the Rhine and the red roofs justifies the climb. Down in the lanes there is a watch-making tradition, and the famous IWC company is based here, though you will not find a shop window as plain as the ones in Zurich.
Just downstream, at Neuhausen, the Rhine drops over the Rheinfall, the largest plain waterfall in Europe by volume. It is not tall, only about twenty-three metres, but the sheer weight of water and the spray that rolls up in summer make a deafening, delightful show. The viewing platforms below the Laufen castle get you close enough to feel the mist, and the whole thing is a short walk from the road. It is touristy, and you should go early or late to avoid the coach parties.
For riding, the real draw is the country north and west of the city: the road to the Wutach gorge and the Black Forest in Germany, with its curving climbs through dark spruce, and the Swiss Jura to the south and west, where quieter roads lead to Passwang. The border here is usually quick to cross, but bring a passport and remember that Switzerland needs a motorway vignette if you use the autobahn, which costs a flat annual fee and is sold at the border and at petrol stations.
Weather swings here are mild, though fog hangs over the Rhine valley on autumn mornings, and the sun burns through by lunchtime.