Genoa, often overlooked, boasts great structures: San Lorenzo Duomo, Palazzo Ducale, Porta Soprana near Columbus' house, Sant' Andrea cloisters. Check our travel guidebook or Google. The city has a bustling harbor, plus beaches and spots like Portofino.
Milan is key in many ways, and I've stayed there often. But after a long trip, your family might prefer Genoa's smaller scale, compact historic center, and diverse sights that suit everyone.
Turin feels more Northern European, French-like, while Genoa has a grittier, Italian vibe. Yet, Genoa surprised me, being more refined and elegant than expected, somewhat like Turin with its arcaded shopping streets and fine palazzos.
Spend two days in this coastal town, then check out other Italian shore villages. Definitely hike from Santa Margherita to Camogli along Portofino's edge.