A couple of years have passed since Genoa’s reign as European Capital of Culture but the effects linger on. The fresh coats of paint on the port-side buildings are still spick and span, and the sheen hasn’t yet worn off the nearly-new Sea and Navigation Museum (Calata De Mari, via Gramsci 1, 010 234 5655, www.galatamuseodelmare.it, closed Mon Nov-Feb), which celebrates the city’s maritime past. Near the museum are the city’s docks – the heart of Genoa and the centre of the local economy. If they look good, it’s thanks to a major restoration by local architect, Renzo Piano. Along with its working port, the town has an ice rink, a cineplex, a vast aquarium (ponte Spinola, 010 2345 666 for tickets, www.acquariodigenova.it) and the ‘il Bigo’ crane, which offers panoramic views over the city and sea beyond. If you can’t get enough of the sea, take a wander on the Neptune galleon docked opposite the Jolly Hotel Marina, which was used as a set in Roman Polanski’s film Pirates.

Above the port is the Palazzo di San Giorgio, a 13th-century frescoed monument to Genoa’s former global influence. It is where Venetian sea captain Marco Polo was imprisoned, and his memoirs recorded; Columbus studied them before setting off.

The city centre is a manageable size but it’s a bit of a steep climb from the port to the old town (centro storico) via narrow, unmapped caruggi, medieval streets punctuated by treasure-filled churches and stylish boutiques. Gorgeous antiques are displayed in the frescoed entrance to a 16th-century palace at Galleria Imperiale (piazza Campetto 8, 010 25 100 86, closed Sun), at the bottom of via Scurreria, off piazza di Lorenzo. Eventually, the caruggi lead to the city’s main squares: piazza Banchi, once a grain market, now filled with flower stalls and second-hand record shops; the revamped piazza de Ferrari, with the Palazzo della Borsa, a major exhibition centre, on its south-east corner; and the neighbouring piazza Matteotti, with the imposing Palazzo Ducale (No.9, 010 557 4000, www.palazzoducale.genova.it, closed Mon), once home to Genoa’s ruler, the Doge, and now an exhibition hall. Rubens has two works in the Gesù church nearby, itself a 16th-century baroque masterpiece.

A little way along, the Cattedrale di San Lorenzo is home to the Museo del Tesoro (010 247 1831, closed Sun), filled with Byzantine trinkets and relics, such as an urn of ashes said to be the remains of John the Baptist. The Palazzo Spinola (piazza Pellicceria 1, 010 270 5300, www.palazzospinola.it, closed Mon) keeps up appearances as the residence for Genoese nobility, and holds vast collections of furnishings, porcelain, silver and textiles. The National Gallery of Liguria (010 270 5300, closed Mon) is located here. A three-day Genoa museum card (€15 from the tourist office) covers admission to most museums. A 24-hour card offers museum admission plus free transport (€10).

• Tourist information: piazza Principe (010 246 2633, www.apt.genova.it); via Roma 11 (010 576 791).