There are a lot of things to do in the Atacama Desert. One of the popular sites is the Valle de la Luna. You can go there on your own or with a tour. Also you have an amazing sky full of stars at night. It's just awesome! Also it's the starting point for tours to the Uyuni Saltflat in Bolivia. We did the tour in three days and it was just great. Just have a Look at the following glott ?
Valparaiso is a really interesting and kreative city. You can explore so much by walking around and because it's built on several hills you have a lot of nice viewpoints there. And don't miss to go up with one of the funiculars which are cheap and a great way to get up the hills.
One of the most interesting spots in Santiago is the Plaza de Armas. You can sit there for hours and just observe the people around. Also it's the starting point to other places to visit in Santiago.
There are some trails at Huerquehue Nationalpark but unfortunately most of them are closed at the moment. If you go there you have to do the Sendero San Sebastian and tell me about it. ? I did the Los Lagos-Trek which was nice but not really spectacular. Some nice viewpoints, nice spots at the lake and a beautiful landscape are good arguments to do that trek. So I had a nice day in the Parc.
I went there by bike and get to the Ojos de Caburgua next to the road. Because of the low season there weren't a lot of people there. So I could enjoy this beautiful spot. You can walk around to some viewpoints and really explore this place. Enjoyed my hour there.
At the pacific coast of the island is the entrance of the national parc which I didn't visit. But I have to the nearby Muelle de las Almas. Really beautiful spot at the rough coast. Nice views over the ocean, the coast and endless forest. Do that instead of the national parc when you are on the island.
From Puerto Montt I made a daytrip to Petrohue from where you can have a nice view to the volcano Osorno. I had really good luck because the weather was fantastic. So I had a great day in Petrohue and the nearby waterfalls. Easy to get there by public Busses.
When you climb up a little bit you can see the mountains which are surounding the City. Nice view and probably the best to do in Santiago. You have the view from Cerro San Cristobal. You can get there by cablecar or, what I always prefer if it's possible, walk up the hill. Try to go there on a weekday otherwise it's pretty crowded.