For first-timers who want to see it all
Start your morning at Piazza Raffaele De Ferrari — grab a coffee at one of the cafés on the edge of the square and let the city warm up around you. From there, make your way down Via Garibaldi, taking your time with the Palazzi dei Rolli. Stop inside at least one of the open palaces.
Mid-morning, duck into Cattedrale di San Lorenzo — spend 20 minutes inside, it's worth every one of them. Then head toward Porto Antico for lunch. Before eating, take a quick look at Vascello Neptune — the full-scale replica ship moored in the harbor is one of those unexpected Genoa moments.
Lunch at Ristorante la Voglia di Genova - A Coae de Zena — proper Ligurian food right by the water. After lunch, walk through the Acquario di Genova or the Galata Museo del Mare, depending on what you're in the mood for. Both are right there, don't try to do both in the same afternoon.
Late afternoon, take the funicular up to Castelletto for the panoramic view over the city at golden hour. Come back down and head to Boccadasse for a gelato on the seafront wall as the sun goes down.
Dinner at Ristorante Trattoria da Maria — cash only, get there early, eat well.