The peninsula is small enough that a scooter or buggy covers it comfortably in a day. Buggy rentals are everywhere in the centre and are the most popular way to explore the more remote beaches. Taxis and app-based cars (Uber operates here) are a cheaper option for getting between town and the nearer beaches.
Walking is perfectly feasible in the old town — Rua das Pedras and the Orla Bardot waterfront are best explored on foot. For beaches further along the peninsula, you need wheels.
Boat taxis and schooner tours offer another way to move between beaches, and they also give you views of the coastline that the roads don't.