And Yahweh God planted a garden in Eden, in the east
Four rivers are named as flowing from the garden of Eden: Hiddekel, Pareth, Gihon, and Pishon. The Pishon's location is unknown, but the statement in Genesis 2.11 that it runs around the land of Havilah suggests it is in or near southern Arabia (per other references to Havilah in the Book of Genesis and the Book of Kingdoms).
The Gihon is likewise mysterious, said to flow 'around the whole land of Cush'. One ancient source, Josephus, identified the Gihon with the Nile. Because 'Cush' is a named used for Ethiopia in the bible, the river is sometimes identified with the Blue Nile river, a tributary of the Nile. The other two rivers, the Hiddekel ('which flows east of Assyria') and the Pareth, are universally accepted as the Tigris and Euphrates.
Eden's garden is in particular thought to come from the sort seen in Mesopotamian kingdoms, temple gardens and royal gardens, with scholarship leaning to the latter type of the two.
In my view, the so-called royal garden provides the most appropriate parallel. Assyrian kings like Sargon II and Sennacherib planted wonderful parks outside their capital cities, Dur-Sharruken and Nineveh respectively. These were places full of all kinds of trees. [...] Seen from this perspective it can be said that in Gen. 2-3 God is the king who planted his royal garden. It is only natural then to read in Gen. 3:8 that God was walking in his garden, in the cool of the day. The garden in Eden is a royal park.
Van Der Kooij, 'The Story of Paradise in the Light of Mesopotamian Culture and Literature',
Genesis, Isaiah, and Psalms, 9-10
A problem for the story in Genesis 2-3 is that there is no place where the Euphrates, the Tigris, the Nile, and a southern Arabian river all converge. In fact, none of them converge together anywhere.
A possible cognate for eden is Sumerian edin, Akkadian edinu, 'an arid "plain" or "steppe," or even "desert," especially one between two rivers' (George & George, The Mythology of Eden, 115). If this is the case, the word has been received into the Genesis 2 myth as the homophone eden (delight), crafting a pun on the garden being watered by an ed (mist) in Genesis 2.6. This gives us an idea of what the 'garden' in Eden may be looked like to the mind of the ancient authors.
Interestingly, Ezekiel twice associates Eden with the region of Lebanon. First he metaphorically identifies the king of Tyre with a cherub 'in Eden, the garden of God' (28.13), and later he either parallels or equates 'the trees of Eden' with 'the choice and best [cedars] of Lebanon' (31.9,15-18). These are the only pre-exilic biblical references to a 'garden of Eden' outside of Genesis 2, and it is notable that Ezekiel only mentions it when talking about Lebanon. Is that where Ezekiel thought Eden was, that the garden was Lebanon's cedar forest, or was he only making a comparison between the two?
Another question is what the phrase 'in the east' in Genesis 2.8 refers to: is it saying that the garden is east within the land of Eden, or that Eden altogether is east (of the author and his original readers)? Neither is compatible with Ezekiel, if he was intending to identify the garden of Eden with the cedar forest of Lebanon.
The best sense we can make of Eden's location is the progression of geography in Genesis 2-11. Adam and Eve are exiled out of the garden eastward, though they remain within the land of Eden (3.24); Cain is exiled farther eastward, finally leaving the land of Eden for the land of Nod (4.16); the post-flood population comes from the east to build the city of Babylon in the land of Shinar (11.1-2). If Ezekiel's comments are intended to identify Lebanon with Eden, we could only determine the traditions of Eden came to Ezekiel in a different form than what is found in Genesis, because it does not match geographically.
Between the information provided by the four rivers and the reference to Babylon, 'Eden' in Genesis 2-3 is a highly mythologized Mesopotamia, with either Eden generally or the garden specifically somewhere east of the land of Israel. It was intended to be understood as a royal garden (possibly with elements of a temple garden), with God as its king, and Adam as the caretaker.