Hello there !
* From Santiago, you could go to the Aconcagua National Park to hike to see the South Face. You start from Puente del Inca in Argentia, right after the border
* More south you can go to the Lake District
or Isla Chiloe
That requires a night by bus or a flight to Puerto Montt.
* Then you can go further south on the Carretera Austral to hike in the splendid Cordillera Castillo
You need to fly , by bus it would take too long !
* And finally of course, you can go to Patagonia, to visit the Torres del Paine National Park and the Fitz Roy area in Argentina
Feel free to contact me, as I spend quite a bit of time in Southern Chile travelling and Hiking.