I have already described one way for the people of Kotor to witness the sunset: to climb up Mount Vrmac, the mountain that stretches into the Bay of Kotor from the left in the first two photos.
The other possibility is scaling the steep mountain behind Kotor, where the deserted villages of Big Zalazi and Small Zalazi are in wonderfully peaceful valleys. From there, you have views like these:
The Happy Hermit 
I totally want to go there, but if I do go, it’ll be on my bike. Not sure yet if the terrain allows for reasonable cycling.
Well, you will have lots of beautiful serpentine roads!
Or alternatively, you could always stay close to the coast and explore the whole Bay of Kotor and the Adriatic coast like that.