Monte Tarn is a full-day hike south of Punta Arenas, on the Brunswick Peninsula near the end of the southern road. The appeal is very Patagonian: open wind, peat, low forest, and broad views over the Strait of Magellan when the weather decides to cooperate.
The mountain also has a small place in exploration history, as Charles Darwin climbed in this area during the voyage of the Beagle. Treat it as a proper outing rather than a casual viewpoint: conditions can be wet, exposed, and cold even when Punta Arenas itself feels manageable.