Slakki zoo is amazing for children, but my favourite is still the Family Zoo and Park in Laugardalur.
I think it has mostly to do with the area, Laugardalur is filled with fun activities, and you can spend the whole day there. You have the Laugardalslaug swimming pool, which I think is the largest one in Reykjavík. It has a few slides and several hot tubs. There are the Reykjavík Botanical Gardens with an amazing café. And of course the theme park with rides for young children.
Also in the area are numerous cafés, restaurants, ice-cream shops and a hot dog stand.
A fun story. An animal escaped the zoo once. Good thing the zoo isn't filled with lions and tigers. No, this was a baby seal that managed to escape and entered the nearby camping area. Visitors woke up in the morning seeing this cutie in front of their tent. I've been told the security is tighter now