Hello! I would say that A is incorrect. In the sentence "I haven't traveled overseas before going to NYC" the part "before going to NYC" is speaking about something that happened before something else in the past and the first part "I haven't traveled overseas" sounds like it is a negative in the perfect present tense. I would also say that B isn't quite right either, because the tenses in the two parts of the sentence also don't match. In the sentence "I haven't traveled overseas before I went to NYC" the second part "before I went to NYC" is perfect past tense and "I haven't traveled overseas" is a negative of the perfect present tense. I would write the sentence as follows: "I hadn't traveled overseas before going to NYC" I hope that helps!

I would say that either ending is acceptable. I think either sentence would make more sense with "hadn't" as the verb (I hadn't traveled overseas before going to NYC//I hadn't traveled overseas before I went to NYC). Either way, your idea is communicated!

In both cases you need to use "hadn't" not "haven't" because the state (of not travelling) no longer applies. It is further in the past. Prior to your trip to NYC. If you are interested in the difference between "going to" and "went to" then the answer is that both can be correct. Personally, I would choose 'going to' if I wanted to say something about the time of that trip - something like "I hadn't travelled overseas before going to NYC, so I was very nervous whilst I was there." And 'went to' for something that happened after the trip - something like "I hadn't travelled overseas before going to NYC, and I felt much more confident about travelling after I went there." - BUT I'm not sure that is a strict grammatical rule. Maybe just a preference?