Genoa

Palaces that 16th-century nobles built in a row line Via Garibaldi, a World Heritage listing since 2006. The Rolli were the republic's lists for lodging state guests among these houses. Interiors kept shut most of the year open only on a few Rolli Days.

One ticket covers the three Strada Nuova museums, and Palazzo Rosso lets you climb all the way to its roof terrace. From the narrow rail at the top of an iron stair, roofs, harbour and lighthouse lie below at once. Anyone afraid of heights will struggle.

Caruggi is the Genoese word for the narrow alleys packed through the old town. Tall houses let in hardly any sun, so they stay cool even in midsummer, and small shrines to the Virgin sit at corner after corner. Map apps often lose their way here.

A cathedral in stripes of black stone and white marble. In 1941 a shell fired by a British warship came through the roof without exploding, and it still sits in the right aisle. The treasury below needs its own ticket.

Built in 1992 for the Columbus Expo as part of Renzo Piano's makeover of the old port, it is Italy's largest aquarium. Dolphin and penguin tanks follow one another inside a ship-shaped hull. At weekends and in school holidays, timed tickets go fast.

A small fishing village surviving at the eastern edge of the city, its painted houses ringing a pebble cove. Walk the Corso Italia seafront to reach it; at sunset many sit on the breakwater rocks with a gelato. Parking is almost nonexistent.

A 19th-century cemetery covering a whole hillside, its galleries filled with life-size marble figures ordered by rich families. The republican Mazzini lies here too. Its sheer size means a particular grave stays lost unless you pick up a plan at the gate.

The harbour light, rebuilt in 1543, is among the oldest in the world still working. You reach it by a long walkway beside the port, and the tower and museum keep short weekly hours centred on the weekend, so check ahead. The climb is dizzyingly long.

From a tunnel off Piazza Portello, an Art Nouveau lift of 1909 lifts you to a hilltop terrace within seconds. An ordinary bus ticket covers the ride, and from the terrace the old town's roofs unfold beneath your feet.

A medieval abbey hidden in a cove of the Portofino headland, with no road: you come by boat or on a mountain path. A bronze Christ was sunk 17m down in the bay in 1954, drawing divers and snorkellers. Boats stay in port when seas are rough.

Where the doges lived and ran the republic, now a venue for major exhibitions. One courtyard opens straight onto the fountain of Piazza De Ferrari. The Grimaldina tower rising at the back long served as a jail for political prisoners.

In a glass block on the old port, a full-size 17th-century Genoese galley lets you climb to the rowers' benches. A floor recreating emigrant-ship steerage lets you trace Italians who sailed to South America. A retired submarine is moored at the quay.

Genoa built this gate in 1155 to hold off Barbarossa; two round towers flank the arch. Just below sits a small ivy-clad stone house said to be where Columbus grew up, though what stands now is an 18th-century rebuild.

A funicular from Largo della Zecca climbs to Righi, a little over 300m up. From the top, old walls and forts run along the ridge, making a full-day walk. Ordinary city bus tickets are valid on it.

From Nervi station, at Genoa's far east end, walk a clifftop promenade running about 2km above the rocks. The old villa gardens above it have been joined into parks, with a rose garden in bloom by May. On rough days spray breaks over the path.

A train ride of half an hour east from Genoa, this fishing village lines its shore with tall narrow houses in varied colours. Some windows and balconies are only painted on. At the May fish festival, fish are fried in a giant pan and handed out.

A village of pastel houses and yachts around a harbour piazza in a small bay. You arrive by bus or boat from Santa Margherita Ligure; drivers leave their cars in a garage before the village. Walk up to Castello Brown above the port to see the whole bay.