The UAE has a number of zoos, many of which are supposed to be pretty good. While I haven't been there, my kids have been to the Kid's Park Zoo for school field trips. From, what I've heard, this zoo is pretty good with play areas for kids and a variety of animals.
The best zoo in the UAE isn't in Abu Dhabi city, it's in Al Ain, a city in the Emirite of Abu Dhabi. The Al Ain Wildlife Park is a great place to relax and is a pretty good zoo. They also have special exhibitions like the animatronic dinosaurs. There is a pretty good selection of wild cats like lions, cheetahs, and leopards. The less predatory animals have a free range to roam. One thing can be said for the Emiratis, they like their exotic animals.
Unfortunately, even with the great zoos in the UAE, there are a number of "private zoos" created through illegal traffickng. Many people may remember the story of the cheetah roaming the streets of Abu Dhabi from May of this year. That was a funny sort of story that made international headlines, but it wasn't an isolated case. December of 2010, a similar case happened in Sharjah, one of the northern emirites. Animal trafficking has become so prevalent in the UAE that the head of the Dubai Zoo has called for a regulatory body to crack down on the practice.
That aside, there are a lot of little mini zoos in surprising places, like Dreamland water park in Umm Al Quwain or Khalifa children's park. Sometimes there are little petting zoos outside of museums for no reason or in cultural villages. Many festivals will provide camel rides or pony rides. The Emirati cultural love of animals helps to ensure that children living in Abu Dhabi will have plenty of exposure to them.