This is confusing! I would agree. It should be, Me gustaría ir al jardín botánico, in order to match the English translation below. When I read the original phrase, I said to myself, "I would like to go me to the botanical garden??" *laughs*
According to Google, it means, "I wish I go to the botanical garden." Translated, that's supposed to be Deseo que yo voy al jardín botánico. That makes no sense either. Further proof that Google isn't always spot-on gramatically...
Perhaps it is just a typo. I haven't seen another instance where they used "Me gustaría ir al ______" with a yo in there.
Maybe Marie could enlighten us?