One of the first things I did when I got to Ubud was go to Monkey Forest! Although it's a super touristy thing to do while there, I wasn't going to miss out on the chance of seeing all of these monkeys living in the forest.
Situated right at the bottom of Ubud, it's a large forest where the Balinese monkeys are semi-wild. Although they are fed in the forest and you can see a few fences, the monkeys would still be able to leave if they wanted to as it's open air. As all of them will have been born there, it will be home to them and monkeys are known to be quite territorial.