I might be missing something I've seen, but here is the list of series off the top of my head...
Tokusatsu: (I try to mark out specific instances anyway.)
Ultraman Tiga:episode 30 - Daigo and Rena's date, which she asked him since episode 25.
Ultraman Nexus: Komon and Riko - recurring in the few early episodes, I believe. (Spoilers for episode 26+) And that place Ren works at, is that a zoo? I can't remember, though I'm leaning more toward it being an amusement park. But whatever that place is, Ren and Mizuho don't really go on a date anyway.
Kamen Rider Den-O: I think episode 42, but don't quote me on it.
Mahou Sentai Magiranger: Episode 47, I think. Urara and Hikaru (with the rest of the family
Manga: (I mark these out too, even though I wonder if anyone is familiar with any of these manga.)
Yume Made KISS: volume 2, episode 5: Yume and Kijinosuke (no idea of the spelling). And not really count since they actually date elsewhere, but Arisu and Kanoko do come to the same zoo, too, if only briefly.
Boku to Kanojo no XXX: volume 4, few episodes toward the end. Momoi (Akira) and Senbongi.
(Special note: These two manga contain my favorite element: gender-switching. And I'll be pleasantly surprised if anyone reading this has ever heard of Yume Made KISS before.)
(And this one is kind of not really related, but I'll put it in anyway since I'm just reminded of it...)
Otomen: Asuka and Ryo's first date is, I believe, in volume 1, chapter 4, at Zoo Need World (sorry, I think it's more of an amusement park, but with that name I could not resist), where Asuka spends time playing a hero and stops a rampaging bull (ah, Zoo Need World has a bull, so it might sort of qualify as a one animal zoo?). (Added March 23, 2011)
The thing I like is, these series do not just put the characters in the zoo (for whatever reason) and have them uninterested in their surroundings. The characters all seem to have fun, which is the reaction I normally expect out of people when they go to the zoo. I think their use of the zoo as almost a character in itself is probably one of the reasons these series stand out in my mind (as in, I have no trouble recalling them for this list).
P.S. I list the names only if at least one character in the pairing is the protagonist of the series (sorry, Yuto (not main character from Den-O)). I usually list the male name first, but in some case, I list the female name first if she is the protagonist and the male is not (or not yet known to be one).