Napier's beaches are more about scenery than swimming. The main beach along Marine Parade is a dramatic stretch of grey pebbles facing the open Pacific -- beautiful to walk along, but the surf is rough and unpredictable, and the stones make for uncomfortable sunbathing. Locals swim here, but it is not a beach for casual paddling.
Westshore Beach, north of the port, is a better option. The sand is finer, the water calmer, and there is a pleasant estuary walk nearby. For proper golden-sand swimming beaches, head south to Waimarama or Ocean Beach, both about 30 minutes from town.