The Chattanooga zoo is by far the smallest zoo that I've ever been to, but they do a lot to make it a fun place for children and families. You will not see all the animals that you do at a big city zoo, but they do have some monkeys, a jaguar, lots of birds, and a petting zoo with sheep, goats a potbellied pig and other animals. The zoo also has several special events throughout the year that are worth going to. Admission is also pretty inexpensive, so you can take the whole family without going broke.
The zoo is located within Warner Park, and can be a bit tricky to locate, but just follow the signs once you enter the park and you'll come across it eventually. Parking is free and you're welcome to bring strollers into the zoo.
All in all, it's a fun place to take the kids for an afternoon.