The Reykjavík Zoo and Family park is called "Fjölskyldu- og húsdýragarðurinn" in Icelandic. There are two joined parks, one for the domestic animals and the other one is a kids' amusement park. They are located in Laugardalur valley, next to the botanic garden there.
At the park city-children can learn about what life at the farms is like and it is VERY popular. All the animals are cared for by educated farmers, so they are set. The domestic animals at the Zoo are sheep and goats, cows and horses, pigs, rabbits, chicken and turkeys, geese and ducks. The wild animals are minks and foxes, reindeers, seals and wild-birds. There is also Science-world and an Aquarium with fish from the N-Atlantic ocean, a restaurant and a small train which drives you around. In the Zoo there is also a "rehabilitation center" for injured or ill wild animals before they are set free again. On the other side of the bridge is Fjölskyldugarðurinn - the family amusement park (see my next tip).
The Zoo is open every day from 10-18 (17 in the winter time) and the entrance fee is ISK 750 for admission to both parks. Kids from 0-4 enter for free and kids from 5-12 pay ISK 550.
I have added more pictures in a travelogue of the animals with their new-born.