I’m chilean and I live in Santiago..

About galleries and stuff, if you don’t have that much time, then don’t go. Nowadays there’s none worthy show in any museum here…Museums in Santiago aren’t that good. But downtown near the Museo de bellas artes, is really pretty; cerro Santa Lucia, Lastarria ST. and the Forestal Park are nice. Though if it’s raining don’t go haha.
Nightclubbing can be risky in some neighborhoods like Bellavista or Suecia, but there are some really good and hip ones around. It depends in your age though, I’m 19 so I don’t know where adults go, but I can tell you that there are some great bars and discos in Santiago; just ask.
Pucon is incredible, I love that city. There are some good bars too there, but the best things there are the lake and all the outdoor sports spots there. I recommend going to one of the springs that are near Pucon :)

Since you’re coming during the winter vacations, I don’t think the subway will be as crowed as is it the rest of the year; it is a great way of moving through the city, is modern, clean and fast. Taxis are a good option too though they’re more expensive of course.

Between cities buses are the best option; TurBus goes from Santiago to everywhere in the country and there are some buses that are super-comfortable (the best way of traveling south is in nightime, because distants are long). Air is a good option too; I know that you can go from Santiago to Pucon by plane, in LanChile (which rocks), but obviously going by bus is way cheaper than on plane.