For me, the best time to go up Monserrate is right before sunset. That way you get to see the view both during the day and at night. If you're lucky, you even get to see an amazing sunset.
Each time I climb the mountain I am welcomed by a unique experience, and tonight was no exception. I don't think I've ever been up there on a Monday night before. It was so peaceful. A little surreal. A sword-billed hummingbird welcomed me as I got off the tram, night jars called in the distance and some even flew above my head before letting me get close enough to take a few shots. A group of friends sat on the steps leading up to the sanctuary, one strumming on a guitar while the others sang along. City lights flickering down below. Beautiful. Every part of it.
I highly recommend paying a visit to the sanctuary at night. The tram runs until 11pm and there is a free shuttle service that will drive you back down to Las Aguas station so you don't have to walk back in the dark. It gives you the opportunity to enjoy the romance of city lights while listening to the sounds of nature in silence.