Five places to see:

1. The Cathedral of San Lorenzo
2. Old Port + Acquarium + Galata, Museum of the sea
3. Palazzo Ducale
4. Via Garibaldi, the 'new street' of XVII century
5. The Nobles'Palace in the Old Town

Five things to do:

1. Taste the local food delicious 'focaccia'
2. Go into a 'Sciamadda' taste 'farinata' (a local food made from chick-pea flour and cooked like pizza)
3. Boat trip to San Fruttuoso di Camogli and Portofino
4. Boat excursion for whales and dolphins spotting
5. Walk up to the ancient Genovese Fortresses

... this is only a foretaste of what Genoa can offer; we are available for suggestions and itineraries.