I was never on this side of the Cordillera (several times in Patagonia but on the Argentinian side), but I think that Torres del Paine is a must. I think it is not very difficult to find how to go there from Puerto Natales. Probably people at your hotel can give you good information about this.
Enjoy Patagonia....is something magnificent and special...on both sides of the Cordillera...
Agustin