These sentences both have perfectly acceptable grammar, but the intended meaning is not entirely clear. Consider this phrasing:
I have some long-lasting memories in my mind, such as memorable overseas trips that I have taken.
The phrases "been through" and "gone through" both can be used to imply enduring hardship or undergoing stress. People use them in sayings like "He looks like he's been through hell" or "I can't believe I had to go through that" or "Don't make me go through that again." This puts a negative connotation on the phrases.
If the overseas trips were negative experiences, if they went badly and are not fond memories, that phrasing is perfectly suitable.
If the overseas trips with enjoyable experiences, saying you "took" a trip is more common and clear.