gittiğinde why de?
Think of it as "at (the time of) your going" -- the de is like the at here, and conveys a "when" meaning.
how to say:
"Owls visit the zoo that you go to"
Baykuşlar, (senin) gittiğin hayvanat bahçesini ziyaret eder.
And don't forget to pay your respects to Duo :)