The correct sentence is, I haven't been to the zoo for ages.

"in the zoo" would only be... 70 % correct. It's the same as "at school". You also can say "in school" but that would refer to the building, not the institution. (at the opera, at the cinema, at the theatre,...) There's an exception: With "at school" you can leave out the "the" (at the school). "At the opera" or "at the zoo" always has a "the". "a zoo" is correct if you want to express that it's any zoo. When you are talking about a specific one or the only zoo in town you have to say "the zoo".

I guess in most cities that have a 'zoological garden' (the old, old phrase, now shortened to 'zoo'), they'd have only one. So 'the' zoo is specific, since you wouldn't have an option of several zoo's. (Was that final apostrophe correct? hmmm) We normally say "I haven't been to the zoo in ages" - this emphasizes the going element ('go to the zoo', ie. a day-trip). "At the zoo" emphasizes you being there. "In the zoo" isn't so common, but I don't see a problem with it - it just focusses on being physically inside the zoo instead of standing at the gates outside. I think it's a matter of taste on which one you use.