Hai Park Zoo in Kiryat Motzkin (in the northern Israel, very close to Haifa) is a very nice mid-size zoo. It does not focus on native fauna (though there are ibex, gazelle, etc.), and has many ABC species (including Asian elephants, giraffes, orangutans, zebras, kangaroos, etc.). But the collection also includes some species which are not present in the US - Mexican spider monkeys (Ateles geoffroyi vellerosus), silver marmosets, white-lipped tamarins (this zoo has a good marmoset/tamarin collection), larger hairy armadillos, cusimanse, yellow mongoose, good collection of parrots (in general, Israeli zoos love parrots. Almost every zoo I've been at, except those that are focusing on native fauna, had very diverse collections of parrots - something that I think is rare in the US)
Further north there is a small Nahariya Zoo, which does not have many large animals (the largest species during my visit in 2015 were addax). When I visited it back in 2015 the zoo had, despite it's very small size, an extremely good collection of small birds - native and exotic - displayed in very nice and photography-friendly aviaries. Many of these species (could not be seen anywhere else. The collection of native snakes was also very good (Palestine vipers, Sinai desert cobras, horned vipers, saw-scaled vipers, etc.). However, since my 2015 visit the zoo's curator changed, and I've heard that the collection nowadays is not nearly as impressive and shifted toward more common pet-store species.