The Spianata di Castelletto is a public terrace on the hillside above the old city, reached by the Portello funicular from Piazza del Portello (a short walk from Via Garibaldi). The view from the terrace looks directly down over the red-tiled roofs of the caruggi to the port, with the sea beyond and the hills on either side.
It is the best viewpoint in Genoa that doesn't require significant walking. The funicular runs until midnight, making it an excellent destination at dusk or after dinner. There is a small bar at the top that operates in summer evenings — a good place for a beer with an exceptional view.