As mentioned, the Prospect Park Zoo is located in Brooklyn so will be the easiest for you to reach most likely. It's not large but has a great collection and is a really underrated little zoo imo. In the past I have combined it with both Central Park and the New York Aquarium, though not at the same time. It's possible to do all three in a day, I think, but I wouldn't recommend that for a first visit. I have combined Central Park Zoo and the American Museum of Natural History before as well; the walk between the two cuts through Central Park itself which it cool in its own right.
As others have eluded to, CPZ can be a bit underwhelming unfortunately. It's nice, but it seems to lose more and more species each year. Currently the main highlights would probably be the Grizzly Bears, Plum-Headed Parakeet (if it's still alive), Yellow-Crowned Gonolek (if it's still alive), White-Fronted Amazon (if it's still alive), Chinstrap Penguin, Atlantic Puffin, Long-Tailed Duck, and Pink-Eared Duck which still makes for a nice selection. The aquarium is lovely, but still under repairs from Hurricane Sandy back in 2012. The main exhibits have mostly reopened and the brand new Ocean Wonders: Sharks! is pretty fantastic. Queens I've only been to once and it's very nice but also small. For a Brit, species like Pronghorn, Chacoan Peccary, North American Cougar, Canada Lynx, and Thick-Billed Parrot are probably the highlights. There are some native passerines int he aviary as well but not sure if there's anything there you couldn't see wild fairly easily (I also don't know if the natives are actually wild or not). Unfortunately the Coyotes are not pure and actually CoyoteXEastern Wolf hybrids.
I can't really tell you where I think you should prioritize simply because I do not know your interests or your zoo visiting style. Hopefully the above can help guide you to a decision, though. Hope you have a good trip!
~Thylo