Given most Biblical events take place in the middle east, probably the middle east!
On the other hand, there's no good evidence that the Ark was even built at all, so it's hard to say where it was built.
The Bible gives no indication at all as to where the Ark was built. Certainly the surface of the earth was drastically restructured by the flood event and so the pre-flood world would have little or no resemblance to the pre-flood world anyway.
There isa no indicatoon that the flood drastically altered the surface of the earth.
We need to separate fact from fiction here. In the story of the bible there is no place where it states the Arks origin. But as this is a story it really doesn't matter
Mt Arrarat references have to be taken with a pinch of salt. Firstly because modern scholars believe that current mount Arrarat was perhaps not the one mentioned in the Bible. Secondly, The mountain was not THE highest one, simply the highest in the region. If you believe the Earth was covreed with water then Everest at 29,000 feet has to be the real peak (If you believe the story Everest must have existed as water erodes and does not build mountains up)
Nobody has 'proven' the resting place of the Ark. There have been no comments from Christian astronauts. Either way you do not need them as the Earth has extremely detailed satellite mapping. The current mapping does not fit in the slightest with the proposition written above.
The place that people do sometimes point to on Arrarat is a formation of rocks that happens to be a rough chape of a boat. This is just a lucky formation of rocks - if you drop them all over the Earth as Nature does then some will look like a boat (how many times have you seen shapes in the clouds). There has been no wooden evidence found.
The story of the Ark is also counter to not one, but every scientif branch and fact we know. Cosmologists know the age of the Universe to be around 14.5 billion years old (BTW the sub-atomic particles in your body were around at the Big Bang so you could glaim to have been preset at the Big Bang).
Dendrochronolgy also points to a much older Earth. Radiological studues show the Earth as about 4.5 Billion years old.
My point is that not just one, but 20+ ways of measuring short medium and long term time all agree on these. None back up the biblical account in the slightest.
Some other thoughts for you. Noah took no fish. So what you say? Well, salt water fish wont survive in fresh water and visa versa. The large amount of fresh water would have killed pretty much all fish
Where were the insects? There are many more species of those than any other animal type and they will not survive without land.
There are too may ways to shoot down anybody who wishes to believe this as fact.
If you are religious then I ask... didn;t Jesus clearly show he jnew what a parable was? Could this not simply be a parable?
And finally for those Creationists out there I have a question. Which Creation? Genesis documents TWO creation stories that are quite different. The first creation is effectively ignored by the second which occurs just a few verses later.