My own little "short"list
Chimp Island
Possibly the most underrated enclosure at Chester and the UK in my opinion. Not much is said about it because it is in the shadow of the impressive RORA, but I don't think there is more heavily planted chimp enclosure in the country. Home to a very large, active group and the indoor accomodation is good despite most of the indoor are being 20 years old.
RORA
The most expensive exhibit at Chester and it allows the inhabitants to act as natural as possible. Home to two successful breeding groups of Orangs it provides an intriguing exhibit for both the public and animals. The "sideshow animals" are also interesting in very good exhibits.
Condor Cliffs
A converted bear pit and can be viewed from "canopy level" and at the foot of the cliff. The base of the exhibit is also one of the most relaxing areas of the zoo because visitors will usually rush towards the giraffes, butterflys or cheetah. Home to Andean Condor and Black Vulture (?)
Cheetah
Excellent cat facility which does a good job of recreating an African Savannah due to Chester's use of landscaping and planting. Visitors can also get great views in a number of locations.
Tropical Realm
Old exhibit, but still going strong and home to some hidden jewells in Chester's collection. Recently upgraded with the addition of a modern crocodile pool
Tsavo
I'm including the aviary and meerkats as well as the Rhinos. A scenic setting for Chester's black rhinos which is complemented well by an excellently decorated walk-through aviary and a good spacious meerkat enclosure.
Twilight Zone
Possibly the largest walk-through bat cave in Europe which houses a staggering number bats (from multiple species). Some intriguing "sideshow animals" also capture the visitors attention.
Bears
A brilliantly landscaped enclosure which has hill, rocks, waterfalls, pools and climbing poles. The bears and coatis can get out of view if they want as well.
Jaguars
Moreso the tropical half, but an excellent facility for displaying these cats. The forest half of the building does a good job of immersing people into the habitat and the leaf-cutter ants make a good distraction if the Jags are a no-show!
Monkey Islands and Mini Monkeys
Monkey Islands is the best set of monkey enclosures i've seen and until recently didn't get enough coverage on this site in my opinion. The islands are densley planted with many climbing poles and the indoors allow for a lot of enrichment to be used and the woodchip floor is a great idea.
Other contenders:
Okapi
Islands in Danger
Elephants of the Asian Forest (the house)
Europe on the Edge
Lions