Re: Chile Lake District?
Wonderful place to visit! You should have a car, however. A few years ago we flew to Puerto Montt, rented a car there, and spent about 3 wks driving up to Santiago. (Which can be done in as little as two days.) Nice people, gorgeous countryside. It helps if you speak even a little Spanish.
Memorable places: Island of Chiloe (just off Puerto Montt), Pucon, Valdivia, wine country (Santa Cruz). Remember that it's only about 100 miles/220 kms from the mountains to the sea, so you have quite a variety of landscapes.
We went in late Feb/early March for the wine harvest.
Have fun!