I would have to say the best designed exhibit in terms of the environment for the animals and the realism of the exhibit for me has to be the Safari at Disney's Animal Kingdom. When I went, the stunning attention to detail, the absence of any visible barriers and the amount of space given to all the animals, it was truly incredible!
The second would have to be Jungleworld at the Bronx Zoo. The primate exhibits are top notch, full of realistic looking fake trees, lots of vine ropes and crashing waterfalls. The Malayan Tapir exhibit is far too small and uninteresting, just basically a sandy beach with way too much area covered by water, and the glass fronted Black Leopard enclosure is also far too small, but overall it is a truly world class exhibit.
Flamingo exhibit which is part of 'Heart of Africa' at the San Diego Wild Animal park is third because the board walk allows for extreme close up viewing of the flamingos, the whole exhibit just appears completely natural and the birds have tons of space and the breeding mounds are so close to the boardwalk so that a variety of behaviors can be observed from the boardwalk.
Himalayan Highlands at the Bronx Zoo is fourth. The snow leopard enclosures are top notch, surrounded by rocky walls that give visitors the illusion of being in the Himalayas. The snow leopards are often very hard to spot due to their excellent camouflage. The red panda and crane exhibits are also excellent.
Dolphin Cove at Seaworld Orlando is fifth in my list because it contains a very large volume of water, and the design is a sandy lagoon with crashing waves surrounded by palm trees. There is a fake coral reef and a sandy bottom instead of the standard concrete bottomed pools. The dolphins have the opportunity to escape from other dolphins if they feel the need. The opportunity to interact and feed these animals is a unique experience too. It gives the illusion that you are on holiday somewhere in a tropical resort.