Situated on the edge of Frederiksberg Park (you can actually see the elephant enclosure from the park) the Copenhagen zoo is one of the oldest in Europe.
It places a high priority on the quality of life, safety, and health of its animals. You can see this in how healthy, active, and productive the animals are.
It's a great place to explore with the family or individually. One of my personal favorites is the open monkey enclosure. Also, if you have kids make sure not to miss the domestic section that has various farm animals and which is more hands-on.
There are also a number of cafes which are well worth enjoying if the sun is out.