The simple answer is that a good zoo recruits, employs and retains good people. Of course, the same thing can be said about a good army or a good bank or a good college and so on.
To work out a more constructive answer to this question, I imagined myself walking into a zoo that I have never visited before. What am I looking for?
Healthy animals
Well maintained enclosures
Animals kept in appropriate social groups with some successful breeding
Interesting range of species
Well designed enclosures (size, furniture, viewing)
Good facilities for public (car parks, footpaths, maps & signs, toilets, food outlets)
Obvious commitment to conservation and education (talks, signage, guidebooks etc)
Attractive surroundings (exhibits, gardens etc)
Links to conservation projects around the world
I have put these in approximate order of significance, in my opinion. I think they are appropriate for all sizes and types of zoo, although obviously they need to be interpreted in context: for example the Chestnut Centre is a collection of otters, owls and native species - but within those limitations they have an interesting range of species including harvest mice and giant otters.