I don't really know around Puerto Montt, but you might want to consider TORRES DEL PAINE, way down south.
I have no idea about costs though.
TORRES DEL PAINE park in Chile, gorgeous place.
here's a map:
On the argentine side you might want to check out EL CHALTEN, http://www.elchalten.com/index.php
a very popular place in Argentina is BARILOCHE, I have not been trekking there, but have been there and it's a beautiful place, with easy access. http://www.bariloche.org/
Bariloche is on the argentine side, to the right of Puerto Montt on the map. sort of.
If you want to stay around Puerto Montt, though, I really have no idea were you should go, sorry!
good luck with your trip!