Punta Arenas is small and largely walkable. The Plaza, the cathedral, the regional museum, the main restaurants and most hotels are within a six-by-six block area you can cross in twenty minutes. The cemetery and the Monumento al Ovejero are a fifteen-minute walk north along Avenida Bulnes; the Nao Victoria Museum and the airport are out of town and need a taxi or a rental car.
Taxis are cheap and metered, and easy to flag down on the main streets. Most short rides within the centre cost less than 3,000 pesos. Colectivos — shared route taxis with numbers on the roof — follow fixed routes through the city and cost a bit more than a city bus.
For day trips to Fuerte Bulnes, the Reserva Nacional Magallanes or the Otway penguin colony, you'll need either a rental car, a tour, or a private transfer. There is no useful public transport on these routes.