A few things for me:
1. Good animal welfare. This trumps everything else. No matter how well the visitor aspects of a zoo shine and how impressive a species list is, first and foremost a good zoo has the best interest of its animals in mind by providing adequate space, adequate social stimulation, adequate enrichment, freedom of movement, etc.
2. Biodiversity. Zoos should be showcasing the vast diversity of animal life. While zoos can (and should) keep some of those iconic, large, popular species, that shouldn't occur at the expense of keeping a well-balanced collection with smaller mammals, ungulates, birds, reptiles, amphibians, freshwater fish, and invertebrates. Even though I happen to not be a fan of all these taxa, I still think it is important for any zoo to highlight the diversity of animal life and have a wide variety of different species on display. This is also regardless of collection size- a small zoo can be really good and still have biodiversity on display, even if their collection is only fifty species, provided that those fifty species contain animals from across all the taxa I mentioned.
3. A strong layout. While I don't necessarily care how a zoo is thematically designed (e.g. geography vs. biomes vs. taxonomy), I do care that there is a logical layout to the zoo, such that one can see the entire zoo in a logical manner without backtracking.
4. Effective use of space and terrain. Zoos should use the space that they have, and use it appropriately. A zoo with substantial rocky sections should use that to their advantage and house animals that climb on rocky terrain in the wild (e.g. snow leopards, markhor, bighorn sheep, hamadryas baboons, gelada), whereas a zoo that has acres of flat, sprawling grasslands would be wise to invest in an African Savanna exhibit, or other grasslands animals. Zoos that effectively use space, and have exhibits that incorporate into them natural terrain, can make for a really unique and impressive zoo experience.
5. Opportunities to get up close to animals. This doesn't need to be the entire collection, and this doesn't necessarily mean petting, but exhibits that allow for an up close view to animals are really great, in my opinion. Large glass windows looking directly into an exhibit, for instance, or walk-through aviaries with no barriers between visitors and birds, are both great ways for zoos to achieve this, but other ways work as well as long as they minimize the space between visitors and animal exhibits (Note- this does not mean build smaller exhibits so that visitors are closer to the animals. This just means allowing the opportunity for those up-close interactions at exhibits, while still allowing the animals freedom of choice).