If the Euphrates here is the Euphrates we assume it is, then I don't think any of the rivers should be looked for in Arabia, or anywhere south/west of the Euphrates. What leads people to look there is an assumption that this Havilah must be the same one that shows up in Arabia elsewhere in The Bible. But there are two Havilahs in Genesis 10, I feel every Arabian Havilah is of Joktan while this Havilah being close to a Cush could be the Havilah of Cush. In fact it could be in this context Havilah and Cush are different names for the same place existing between the Pison and Gihon.
I've talked before about how Cush wasn't only in Africa, I see evidence to link him to India, and I suspect some of the Indian Cushites were initially in Iran for awhile. This Havilah could perhaps be connected to Ahaz, a name who's etymology is linked to the word "af'āl".
I believe there is significance to the order the rivers are listed in Genesis 2, something most popular theories about them don't consider. Particularly I think it likely they are starting in the East and going Westward. They are listed in the order Pison, Gihon, Hiddekel and lastly the Euphrates. So if that is the Euphrates we assume it is, and the Hiddekel is indeed the Tigres, then the Gihon would be the Karkheheh river and the Pison would be the Karun river, known in classical times as the Pasitigres. Here is a map taken from the Wikipedia page for the Karun.
I'm not the first to propose these two rivers, my exact theory was proposed by at least one prior scholar, and another makes my Pison the Gihon. But some want to take one of these while also trying to place the Pison or Gihon in Arabia. And one website dismissed these two rivers by saying they are too small. But the text of Genesis 2 says nothing about their size, it's merely man's imagination that wants to assume all four rivers were as epic and history defining as the Tigris and Euphrates.
Both of these rivers start in the Zargos mountains, which is why previous arguments for one of them being the Gihon tend to be based on saying the land of Cush in this context is the homeland of the Kassites commonly speculated to come from somewhere in the Zargos mountains. There were also ancient gold mines in the Karun river region.
Al-Qurnah is a place on the Shatt al-Arab that locally claims to be where the Garden of Eden was.
The Karkheh river also plays a role in arguing that the land of Aratta from the Sumerian epics about Enmerkar was in the area of Mt Alvand and ancient Ecbatana, modern Hamdan, which in turn factors into B.J. Corbin's theory about where Noah's Ark landed. His theory also involves using information from Jubilees to suggest the area around where the Ark landed was the ancient settlement of Arphaxad, remember the Book of Judith names the king of Ecbatana as Arphaxad which has always confused scholars.
As interesting as all that is, I remain skeptical of the assumption even that this Euphrates is the usual Euphrates, even this theory that I feel is the most viable one with it being the same Euphrates is still using some other Biblical Names differently from what they usually mean. So it seems odd to act like the Euphrates is the truly indisputable one.
During the Victorian period it was common to theorize Eden was in the area North of India/Afganistan and East of the Caspian Sea. A theory most interesting to me because of how it might have influenced where Tolkien chose to place Cuivienen. This tends to involve a long history of the Amu Darya being identified with the Gihon and the "Cush" in question as the Hindu Kush or the Kushan Empire. But I've looked at certain maps of the Amu Darya and thought maybe it's the main river of Eden and the four rivers are the Surkhan, Vakhsh, Panj and the Kunduz. There are also theories placing Aratta that far east.
I have also looked for Eden in Yemen, theorizing the name is linked to Aden, as well as my belief that Sanaa may be Sinai. Based on this Map of Yemen the best bet for Eden may be north of Sanaa.
Now that I've said all that, I'm gonna go watch an Anime called Eden of Th East.
Update: Out of Africa.
My interest in theories placing Eden in Africa is entirely from my interest in playing Devil's Advocate with Local Flood proponents. So many of these people are selective, ignoring that if they really want to make The Bible compatible with the Evolutionary/Uniformitarian view of Human history you have to place Man's origin in Africa.
Of course one can argue you need a local flood for Eden to still be identifiable with contemporary geography at all. The Global Flood as presented by Ken Ham and Kent Hovind certainly makes it highly unlikely any post-flood rivers are the same. Yet Global Flood supporting literalists like Rob Skiba obsess over the present tense grammar of Genesis 2's language to insist we can still find it.
It is not as necessary for localists to place Ararat in Africa since they can argue it's a local flood that happened after Noah's line had already migrated. In fact it used to be local flood advocates specifically claimed there were no flood legends in Africa, which suited their often racist agenda of denying Africans share descent from Noah (or sometimes even descent from Adam and Eve). But that was outdated research, now many African flood legends are known including a possible Egyptian allusion to it in the Book of the Dead.
It has long been popular to identify the whole Nile with just the Gihon, hence making the Cush/Ethiopia association work with how that name is traditionally understood. But an argument for a Havilah in Africa can work via the Avalites.
What I'm contemplating here is The Nile as the main River of Eden and the four as rivers that flow into the Nile in Sudan. The White Nile and the Blue Nile, the Atbara, and perhaps also a no longer existing river known as the Yellow Nile, a remnant of which is the Wadi Howar. (Or perhaps one is an ancient river where the Wadi el Melik is and the first or last river is the Nile between where the White and Blue meet and where it converges with Atbara.)
The Yellow Nile is generally believed to have been gone by 4,500 BC hence long before recorded history begins. But ancient Greek Geographers believed the Nile originated in what they called Libya (much larger then modern Libya) originating in the Atlas Mountains. The Yellow Nile's existence would not make this mistaken belief entirely correct as it still doesn't start in the Atlas, but it does make more sense out of it since the Wadi Howar is in what's still called the Libyan Desert.
The Atlas Mountains (or beyond them) is also where Greek Mythology places the Garden of the Hesperides, which is clearly their memory of the Garden of Eden. But given this above confusion it could be where they meant to place it was the source of the Nile.
This interestingly places Arabia/Yemen "East of Eden" where the "Land of Nod" was, Nod means wandering, and Arabia is also where I believe the Wandering after the Exodus took place. And Cain is believed to be buried in the city of Aden in southern Yemen.
Thing is, I continue to favor a Global Flood. And I think the present tense language in Genesis 2 is because Moses copied from an older contemporary source that Noah and Shem preserved through the Flood.
Update June 2019: Eden in Israel.
There is also the desire many have to place the Garden of Eden in Israel, preferably in or near Jerusalem. Frequently justified by associating the Gihon of Genesis 2 with the Gihon linked to Solomon's Coronation in I Kings 1:33-45 and possibly mentioned again in 2 Chronicles 32:30&33:14.
Traditionally that Gihon is viewed as being a Spring in what we today call the "Old City" of Jerusalem which is the water source of the traditional Pool of Siloam. That certainly can't be the Gihon of Genesis since it's a Spring and not a River. But The texts of Kings and Chronicles never call it a Spring. And my argument that Zion Which is the City of David is actually Bethlehem not Jerusalem proper gives me plenty of reason to move where the Gihon is. The Gihon issue is one detail I was never able to fully pin down in that post.
If Eden is in Israel then I think the River of Eden is probably the Sorek and the other rivers it's Tributaries.
Based on that map I'd say the Pison and Gihon are probably the tributaries east of Beth-Shemesh and south of the main Sorek, one of them certainty enters into the vicinity of Bethlehem.
This would place both Bethlehem and Jerusalem in the eastern most part of Eden, and then I place where Jesus was Crucified East of Jerusalem, perhaps the same spot where Abel made his Sacrifices. And then the Land of Nod further East could be a wilderness within Israel (perhaps the same wildness often identified with Dudael where the Azazel Goat was sent), or the massive desert between Israel and Mesopotamia.
As far as Cush being associated with the region of this Gihon candidate goes. Egyptian records don't start using the name of Kush to describe people to their south till the Middle Kingdom. So I think it's possible the ancestors of those Kushites were in Canaan originally but then were among those who migrated to Egypt during the seven year famine in the days of Joseph. And maybe that could support an argument for the Babel of Genesis 10&11 or some other city linked to Nimrod being Jebus/Jerusalem?
Psalm 7 is concerning the words of a Cush the Benjamite, who I think is a variation on the name of Kish the father of Saul. The port city of Joppa can be linked to Benjamin via it's link to Lydda, and Greek Mythology where Joppa is part of an Ethiopia.
