I would say that depends on what type of trip you want to do during that time. I was down there last fall semester (that would be fall here in the states) and really liked the lake district and patagonia. Both have amazing sites to see, but could require more time than have. If you want to go south look into the area around Puerto Montt and Puerto Varas and a little bit farther south. Parque Pumalin is supposedly amazing with some amazing old growth alerces. If you want to go north some friends of mine went to Parque Lauca which is up in the altiplano near the bolivian border and their pictures looked very cool, flamingos, large lakes and picturesque stratovolcano's rising from the shores.
If you want to fly when in Chile look into buying tickets on www.lan.com, they usually offer good last minute discounts.
Also if you want to go the touristy route, Pucon is the outdoor sports mecca in chile, climbing of volcán Villarica (an active volcano), mountain biking, rafting, etc.