The correct wording is "This is my first visit TO the USA", or "Is this your first visit to the USA?"
If you are going somewhere, you make a "visit to" that place.
A "visit of" means that the object is visiting you. That is, if you said, "This is the first visit of Uncle Joe", you would mean that Uncle Joe is visiting someone.
You would have to choose #1 , because #2 contains the diparaged construction "the reason why".
However, neither #1 nor #2 is a good rephrasing of the incorrect example.
For one thing, "what is the reason" was changed to "is this the reason", which changes the meaning.
For another thing, "neglecting doing" is awkward. Of course, simply taking out "doing", as user8399 suggests, changes the meaning. "Neglecting to do..." would be better.
For another, If you treat "neglecting" as a noun, it should be your neglecting. . . " rather than you neglecting. . ."
So really, the correct answer is that neither #1 nor #2 is a good rephrasing.
Feel free to tell your teacher this; and that the question should be thrown out (not counted), because it was so badly written; and that you deserve extra credit for this analysis, not a downcheck for whichever answer you chose.
Best Answer
I think the difference is that we use "to" when "visit" is a verb:
and "for" when "visit" is a noun:
Of course, when "visit" is a noun, you will need to add an article before it (Get ready for the visit), a determiner (I am not ready for that visit) or a possessive pronoun like in the example.
If you want to use it without a modifier, then you can do as J.R suggested and turn it into a gerund.