The old town is compact and entirely walkable. Everything worth seeing fits within a 15-minute walk, and the city walls provide a natural circuit for an afternoon's wandering. Flat shoes are useful — the old quarter has a few steep alleys, especially around the cathedral.
Pamplona has a small urban bus network that connects the centre with the newer neighbourhoods and the train station on the southern edge of the city. Tickets are inexpensive and the routes are simple. Taxis are plentiful and not expensive.
During San Fermín, the old town is pedestrianised for much of the festival, and the streets around the encierro route are closed in the early mornings. Getting anywhere by car in July is more trouble than it is worth. Walk, or use the bus.
Cycling is increasingly well catered for, with a network of bike lanes linking the old city with the riverside paths along the Arga. Rental bikes are available in the centre.