Schaffhausen’s lofty Münster zu Allerheiligen (Cathedral of All Saints) is the focus of the Old Town. The first church on the site dated from 1049, very soon after the founding of the town itself, and was replaced in 1103 by the building which still stands today. The beautifully restored Romanesque church tower gives a hint as to the interior (Tues–Sun 10am–noon & 2–5pm), in which twelve huge columns of Rorschach sandstone line the austere, mostly unadorned, Romanesque nave. Beside the cathedral, the Romanesque-Gothic cloister is the largest in Switzerland, a lovely broad walkway circling the Junkernfriedhof, or noblemen’s cemetery, many of whose inhabitants are commemorated on plaques set into the wall. In the cathedral courtyard sits the gigantic Schiller Bell, cast in 1486: its Latin inscription of vivos–voco/mortuos–plango/fulgura–frango (“I call on the living, lament the dead, halt the lightning”) is supposed to have inspired German poet Friedrich Schiller to compose his Song of the Clock … despite the fact that Schiller never set foot in Schaffhausen. Just beyond is the atmospheric little herb garden, precisely recreated according to medieval records.

In the same complex as the Münster is Schaffhausen’s principal historical museum, the Museum zu Allerheiligen (May–Oct Tues–Fri 10am–noon & 2–5pm, Sat & Sun 10am–5pm; Nov–April Tues–Sun 10am–noon & 2–5pm; free; www.allerheiligen.ch). Unfortunately, although the collections are interesting, the desk can’t help out with recent English notes and there’s also been so much reorganization in recent years that the museum’s own plan is out of date. The ground floor is mostly given over to the vast archeological collection but, as with the rambling historical collections spread over this and the upper floors, there’s little coherence. The place is like a labyrinth, and you could either wander, enjoying the surprise of coming across a roomful of early medieval religious art, or a restored Gothic chapel, or a display on Schaffhausen’s military history, or instead cut your losses and head for the topmost floor, which holds an engaging collection of art by Swiss painters and sculptors of the last five hundred years.

Baumgartenstrasse marks the southern boundary of the cathedral quarter. In an old textile factory metres from the river at no. 23 is the Hallen für Neue Kunst (Contemporary Art Spaces; May–Oct Sat 2–5pm, Sun 11am–5pm; Fr.14; www.modern-art.ch). Pricier than it need be, and with awkwardly limited opening hours, this impressive gallery is still well worth a visit, with work by artists, known and unknown, from the 1960s to the present spread over several vast floors. Particularly striking in such airy surroundings are the geometrical games in two and three dimensions of Robert Mangold, and Sol LeWitt’s dazzling cube installations.