Via del Prione is the main pedestrian axis of the old centre, running from Piazza Cavour northwards through the heart of La Spezia. In the evenings it fills up for the passeggiata — Italians of all ages walking slowly, greeting acquaintances, and stopping at bars for the aperitivo hour. It's one of the better examples of this daily ritual in Liguria outside Genoa.
The street has the usual mix of Italian town-centre shops (pastry shops, delis, clothing), but it's the surrounding lanes that reward exploration: small piazzas, a few good restaurants, some serious wine bars, and the occasional medieval tower embedded in an otherwise ordinary building. The churches of Santa Maria Assunta and Nostra Signora della Neve are both on or near Via del Prione and both worth a look.