The second best view of Santiago de Chile can be enjoyed from the Castillo Hidalgo on Santa Lucía Hill. We stayed very close to here so it was only a short walk for us to get up there. There are multiple entry points. We took the entrance at the corner of Victoria Subercaseaux and Sta Lucía.
The beginning of the path goes through a very nice park with exotic flowers and vegetation. The way up to the castle is quite steep and the steps are quite slippery and too far away from each other so best to pay attention when you walk all the way up. The view from the top of the castle is marvelous and it is definitely worth the 15-20 minutes walk.