Alpenstrasse leads from the station past Bundesplatz straight down to the lakeshore jetty from where boats depart all around the Zugersee. Views of the Rigi and, to the west, the Pilatus and Bernese Alps are terrific. Vorstadt follows the eastern lakeshore to Postplatz, on the the edge of Zug’s tiny Old Town.

From Postplatz, Neugasse, lined with shops, leads south to Kolinplatz and the striped-roof Zytturm, at 52m the Old Town’s tallest building but these days tucked into a corner beside a busy traffic road and largely forgotten. Built in the mid-thirteenth century as a watchtower, it was renovated to its present shape in 1557, and endowed with a clock in 1574. The shields below the clock face are those of the eight Swiss cantons at the time of the tower’s construction (from left to right, Zürich, Bern, Luzern, Uri, Schwyz, Unterwalden, Glarus and Zug). As well as the astronomical clock, there’s a host of tiny details on the tower, including, under the archway, a beautiful late-Gothic wavy-haired angel. Just above the upper ledge, you’ll spot a painting of a rat with an interesting history.

Opposite the Zytturm, Kolinplatz features a fountain dedicated to Wolfgang Kolin, standard-bearer of the Swiss army at their 1422 defeat by the Duke of Milan. Heading beneath the Zytturm brings you into the most atmospheric part of the Old Town, cobbled lanes lined with medieval gabled and balconied (and often frescoed) houses. Just behind the Zytturm is Zug’s Rathaus, dating from 1509 and retaining much of its original woodwork, and a few steps north is the waterside Landsgemeindeplatz. From the Rathaus, Unteraltstadt and Oberaltstadt both lead south to the tiny Liebfrauenkapelle, dating from 1266 but boasting a marvellous Baroque interior.

If you follow the alleys uphill from the chapel, and cross the main Grabenstrasse, you’ll spot St Oswaldsgasse leading left to the Kirche St Oswald, built between 1478 and 1545 and dedicated to St Oswald of Northumbria (605–642). Inside you’ll find another lavish Baroque interior and a nineteenth-century mural above the choir of Christ poised above several romantically depicted scenes from the Bible. As you leave, look above the double portal to see a beautiful carved statue of Mary flanked by St Oswald and St Michael. It’s a short walk from here up Kirchenstrasse to the Burg, a circular, top-heavy construction that was once the headquarters of the Kyburg and Habsburg governors, and now houses the town’s museum (Tues–Fri 2–5pm, Sat & Sun 10am–noon & 2–5pm; Fr.5, free on Sun; SMP), worth a look for its historical and archeological bits and bobs and for its model of medieval Zug. A few metres further up the hill is the Kunsthaus, with usually very good temporary art exhibitions. If you head along Dorfstrasse, and across the main Ägeristrasse, you’ll spot a set of quiet, concealed steps leading up to the chapel of a Capuchin convent (1597), with an adjacent, well-tended walled cemetery. Tranquil covered steps bring you down to opposite the old mint, with Postplatz to the right.