Tierra del Fuego National Park
This is only about 15 minutes outside of town and warrants a visit. It can get crowded, so try to go with a company that knows how to avoid the tour busses (I went with Tierra Turismo and they were able to avoid the crowds). Solid hiking trail info is tricky to come across. There are a couple of campsites you can crash at, but you need to be prepared and bring all your gear - there's no refugios. Dress for insanely quick changes in weather - sun, snow, high winds, it's all possible.