A couple of things I enjoyed:
- The Cerro San Cristóbal is absolutely fantastic - amazing views of the city. This is a must do in my mind.
- The Sky Costanera also a fantastic view of the city and it has a sky bar at the top (I believe the building is the biggest in Latam).
- I found the historic centre of Santiago to be a little underwhelming compared to other places in Latam to be honest, but it's still worth going to check it out. The Palacio de la Moneda in particular is cool.
- The Cerro Santia Lucía also has a great view - it's in the city itself, so a different perspective from Cerro San Cristóbal.
- The Museo de la Memoria y los Derechos Humanos is one of the most interesting museums I have been to. It's mainly about the los desaparecidos and other victims of the military dictatorship in Chile under Pinochet.
- If you have time, you can also do a day trip to Valparaíso/Viña del Mar or the Cajón del Maipo (either of these options will take a full day).
Tourists typically stay in Las Condes or Providencia. Both are very nice with heaps of restaurants. We stayed in Barrio El Golf which is basically on the border between the two.