There isn't much to Puerto Natales other than being a gateway to the stunningly beautiful Parque Nacional Torres del Paine. As such, it has a decent selection of restaurants and places to stay along with a rather busy bus station to support all the tourists that pass through.
Parque Nacional Torres del Paine, with its steep, jagged-edged mountains rising straight out of nowhere above lakes, rivers and valleys, reminded me of Grand Teton national park. It's majestic. The massive Paine massif, an eastern ridge of the Andes, is home to the Cordillera del Paine, a series of granite towers as well as several large glaciers including Grey, Dickson and Tyndall. The plains are populated with guanacos, which are protected in all of Chile. If you enjoy serious hiking, this is it.
If you don't hike the park, you will likely join a one-day tour which with inevitably take you to the Mylodon Cave, once inhabited by prehistoric, slothlike mylodons. It's a giant cave. The closet you'll get to anything Mylodon is the giant cement recreations.