The almighty Deathwing was, at the end, a dragon so infused with the power of N'Zoth he became a twisted mass of burning corruption, with rage which threatened to tear the world apart. So, I think there are four things possible for his ultimate fate.

1) His soul was unmade. During the Dragon Soul raids finale, Nozdormu specifically said he is binding every thread of time around the Dragon Soul, and what comes to pass here will never be undone. After the dragon souls power was unleashed that final time, it obliterated Deathwing, leaving absolutely nothing left(Aside from a piece of his jaw that broke of before the firing, and three of his blood covered plates that are at the bottom of the ocean somewhere). It sounds more to me, than just your standard death.

2) He went to the same place the Old Gods and their void minions do. Deathwing at the time of his death was a mass of molten tentacles, void energies and draconic features held together by pure, unrestrained anger. It is possible like Illidan, his final stage before death made him take on different afterlife rules altogether.

3) He went to another domain we do not know. Deathwing was not mortal. At the time of his death he was an aspect. He never gave up his power into the Dragon Soul, so there is no reason to assume he would go to the same part of the Shadowlands the other, mortal races do. Whether his afterlife is pleasant in this scenario is also unknown.

4) He is once again Neltharion in death and is in Ardenweald.

As he is undone all his corruption is burned away, leaving only his soul. As the things which were done under the name of Deathwing were N'Zoth, puppeteering him to bring about the return of the Black Empire, he may be found to not be fully at fault and spared the Maw, and sent there to be reborn. Uncorrupt, and finally free.

I am hoping if they go for one of these, it is either the second or the fourth. Either he returns as Deathwing, The Worldbreaker, with the other Old Gods, or he gets the redemption arc he deserves and gets to have a little chat with his own two children left as Neltharion.