Abbas - Tanwîr al-Miqbâs min Tafsîr Ibn ‘Abbâs
(He said: Go down (from hence)) from Paradise, (one of you a foe unto the other) meaning: Adam, Eve, the serpent and the peacock. (There will be for you on earth a habitation) a dwelling and shelter (and provision for a while) until death.
Said He, ‘Go down, that is, Adam and Eve, with all those you comprise of your seed, each of you, each seed, an enemy to the other, on account of the wrong each does to the another. There will be for you on earth an abode, a place of settlement, and enjoyment for a while’, [until] your terms [of life] are fulfilled.
(Get down), was addressed to Adam, Hawwa', Iblis and the snake. Some scholars did not mention the snake, and Allah knows best. The enmity is primarily between Adam and Iblis, and Hawwa' follows Adam in this regard. Allah said in Surah Ta Ha,
اهْبِطَا مِنْهَا جَمِيعاً
("Get you down (from the Paradise to the earth), both of you, together...'') 20:123. If the story about the snake is true, then it is a follower of Iblis. Some scholars mentioned the location on earth they were sent down, but these accounts are taken from the Israelite tales, and only Allah knows if they are true. If having known these areas was useful for the people in matters of religion or life, Allah would have mentioned them in His Book, and His Messenger would have mentioned them too. Allah's statement,
(On earth will be a dwelling place for you and an enjoyment for a time.) means, on earth you will have dwellings and known, designated, appointed terms that have been recorded by the Pen, counted by Predestination and written in the First Record.
(Thereof (the earth) We created you, and into it We shall return you, and from it We shall bring you out once again.) 20:55. Allah states that He has made the earth a dwelling place for the Children of Adam, for the remainder of this earthly life. On it, they will live, die and be buried in their graves; and from it, they will be resurrected for the Day of Resurrection. On that Day, Allah will gather the first and last of creatures and reward or punish each according to his or her deeds.