The mistake you are making is assuming that “going” in that sentence is a verb. It is not. It is a gerund. A gerund is a word that looks like a verb, but it is used as a noun or an adjective. And on top of that, you are speaking another language with the thought patterns completely different from English.
There are other ways of expression what you want to express. You can never translate word for word. Often, you can’t translate the grammar either. You translate the concept ir thought and express it in the target language the way they express it.
제 (jeh) = my, 가는 곳 (kanun got) = “going” as a noun, not a verb. One way they would express this a little more like 외출 할때 (ohchool halddeh) which is “when I go out.” 외출 하다 is the verb that means ” to go out.” Changing the 하다 (hada) to 할 (hal) makes it prepared to use with 때 (ddeh). 때 is not really “when,” but “time.” However, it makes more sense in English to think of it as “when.”
Another way they would express it is 외출하면 (ohchool hamyeon) means “if I go out.” Again, 외출 하다 (ohchool hada) means “to go out.” You take the 다 (dah) off and add 면 (myeon) which means “if.”
One of the things you need to remember about Korean is that it is not as specific as English, so it is normal to leave the pronouns out. Another things you have to remember is that they use conjugations often when we use words. Many languages including Korean, have a word for “go out,” but English has to use words to express it, and, if you put 밖에 (bakk e) which means “out” after the gerund 가는 곳 (kanun kot), it is just strange because in Korean “out” or 밖 is a preposition, not part of a verbal or gerund.
If you want to learn to speak a foreign language, you have to learn new ways of thinking about things. You need to remember that Korean and English are basically at two ends of the spectrum of languages, and they are so completely different that it is really hard to cross the bridge. I congratulate the person who wrote this question because at least they know how to put together a gerund even if they aren’t sure what it is or how to use it.