They have proposed a few models. The "Out Of Africa" hypothesis is the currently reigning paradigm, though I personally find the "evidence" for an east African origin of humanity dubious at best (It is based around faulty assumptions on genetic diversity). But the science for the core of the "Out Of Africa" hypothesis is sound. Humans originated from a small population in a single location and proceeded to spread around the world.
Here is what the Bible has to say on the Gardens location:
Genesis 2:5-14 "These are the records of the universe at its creation. On the day that the LORD God made the earth and skies, no shrubs had yet grown in the meadows of the earth and no vegetation had sprouted, because the LORD God had not sent rain on the earth and there were no human beings to work the ground. Instead, an underground stream would arise out of the earth and water the surface of the ground. So the LORD God formed the man from the dust of the ground, breathed life into his lungs, and the man became a living being.
The LORD God planted a garden in Eden, toward the east, where he placed the man whom he had formed. The LORD God caused every tree that is both beautiful and suitable for food to spring up out of the ground. The tree of life was also in the middle of the garden, along with the tree of the knowledge of good and evil. a river flows from Eden to water the garden, and from there it divides, becoming four branches. The name of the first one is Pishon—it winds through the entire land of Havilah, where there is gold. The gold of that land is pure bdellium and onyx are also found there. The name of the second river is Gihon— it winds through the entire land of Cush.The third river is named the Tigris— it flows to the east of Assyria. The fourth river is the Euphrates." (Quoted From The International Standard Version)
Here the bible speaks of four rivers, two of which, the Tigris and Euphrates, still exist today and are quite well known in the middle east, notably Iraq. However, the other two rivers are unknown. Bearing in mind the general consensus is that the first five books of the Bible (including Genesis) were written by Moses on Mount Sinai which is most likely in northern Arabia. So that is the reference point for the statement "God planted a garden in Eden, in the east". Fitting quite nicely with the Tigris and Euphrates rivers in Iraq (which is directly east of northern Arabia).
Young-Earth Creationisms Eden:
I will also note that young-earth creationists like to say the gardens location is unknowable because Noah's flood (which they believe is global) rearranged the geography of the Earth. While I do agree that a global flood would rearrange the geography of the earth (though not quite as much as young-earthers imagine, as it wouldn't cause volcanoes and earthquakes, or form mountains), I disagree there was a global flood at all. Noah's flood was likely local in geography but worldwide in judgement on mankind, but that is a post for another time.
In fact, I would say the gardens geography in Genesis 2 provides evidence that the flood of Noah was local rather than global. As Moses refers to the Euphrates river simply as "the Euphrates", meaning he expects the audience to know what river he is talking about, if young-earth creationists were right about a global flood, the sediment laid down by the flood would destroy any rivers or lakes on the surface of the earth.
Now, the Tigris and Euphrates rivers come together in two places, one is in the mountains in turkey, and one is in far-southern Mesopotamia, where they merge into one river shortly before draining into the Persian gulf. This extremely short merged river is called the "Shatt Al-Arab"
We can easily rule out the northern location, as it is at such a high elevation it would be far too cold to match the biblical description. And it would likely be much colder during the time of Adam and Eve, as the earliest evidence for true humans is dated to the midpoint of the last ice-age.
The Last Ice Age:
Scientists refer to this area as the "Persian Gulf Oasis" as the region would have been extremely fertile compared to the surrounding area. Here is a quote from archaeologist Jeffery Rose (As far as I know, he is not a christian and is not aware of the parallels between the Persian Gulf Oasis and the garden of Eden.):
"It would have been an ideal refuge from the harsh deserts surrounding it, with fresh water supplied by the Tigris, Euphrates, Karun and Wadi Baton Rivers, as well as by upwelling springs."
Sound familiar? Here, a secular archaeologist describes four rivers (including the Tigris and Euphrates), an oasis, and underground springs. All three of which are how the bible describes Eden. Furthermore, the Persian gulf oasis is described as a fertile floodplain, and the Hebrew word "Eden" literally means "fertile plain".
Now, is the Persian gulf oasis the garden of Eden? No. The bible describes the garden of Eden as a small place *within* Eden. So small that Adam and Eve could apparently explore it separately and still easily be able to find eachother. The Persian gulf oasis is described by scientists as being "the size of great-Britain". The Persian gulf Oasis was likely the Land Of Eden, with the garden somewhere within it.
Will be be able to find any archaeological evidence of the garden itself? Probably not. The bible describes the garden being burned down by an Cherub ("So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life." Quoted From The King James Version) and then flooded at least twice. (Noah's flood and the refilling of the Persian gulf at the end of the ice age). So, I guess archaeologists should be looking for the gardens...ashes, buried under sediment...which is then covered with the waters of the Persian gulf.
I suppose you could try and find the bones of animals that are not indigenous to that area, as God brought all the animals of the earth to Adam for him to name. But we don't even understand the mechanism of that, did God teleport them? Did he teleport the animals back after Adam named them? Did the animals reproduce and inhabit the area long-term? Its a bit of the longshot, and any remains that exist would still have to be excavated from underwater in the Persian gulf.
Identifying The Pishon And Gihon:
Now, the excerpt from Jeffery Rose described four rivers, two of which are the Tigris and Euphrates. It seems almost certain that the other two are the Pishon and Gihon. But which are they? And do they match the texts description of the rivers?
The Wadi-Al-Baton river does not flow strongly or constantly today, with much of it remaining dry the majority of the time. But during the last ice age, the ice on the Hijaz Mountains in western Arabia (The source of the river) was far more extensive then it is in now. This allowed the river to flow much more strongly then it does today.
Does the Hijaz Mountains region match the biblical description of Havilah? The Hijaz Mountains contain the "Cradle Of Gold", which has been recorded being mined as far back as 3000 BC, and is stilled mined into modern times. It has also been identified as "King Solomon's Gold Mine". The Hijaz mountain is also rich in bdellium plants.
This leaves us with one option for the Gihon, the Karun river. This is slightly problematic as the Karun flows east of of Mesopotamia toward Iran, and the biblical text associates the GIhon with Cush. Cush is typically associated with North-Eastern Africa, west of Mesopotamia, with the red sea flowing between them.
However, no river would fit this version of Cush, as it would have to flow across the red sea into north-eastern Africa. Many modern scholars instead identify Cush with the Kassites in Zagros Mountains in Iran, if this is the case, then the Karun would completely match the description of the biblical Gihon.
If this is not the case, the Karun could still be identified with the Gihon, as an African Cush could have had an undiscovered colony in what is now Iran. For the time being, weighing all the evidence, I would say the Gihon is likely the modern Karun river.
Taking this into account, the garden's location is now somewhere underwater in the northern part of the Persian gulf. Where the Tigris, Euphrates, Pishon (Wadi-Baton), and Gihon (Karun) meet to form the river of Eden (Or Shatt-Al-Arab).
After Adam and Eve were deceived by the serpent and sinned, they were expelled from the garden which was then burned by a cherub. They then migrated eastward, but apparently still stayed in the fertile land of Eden.
Later, when Adam and Eve's son "Cain" killed his brother "Abel" , he left to the land of Nod, east of the land of Eden. Probably in the modern day Khuzestan Province of Iran. The bible says Cain built a settlement there, named after his son "Enoch". Perhaps some excavating could be done there in an attempt to find this settlement.
Adam and Eve's other descendants mostly stayed in the Land of Eden in the time following their sin. Though some of them apparently migrated to what is now southern Iraq (including the ancestors of Noah).
In conclusion, humanity originated in what is now the northern Persian gulf. This is the starting point for all human migration. After Adam and Eve's sin, humanity stayed localized to the land of Eden (What is now flooded with water in the northern Persian gulf), the land of Nod (what is now the Khuzestan Province of Iran), and what is now southern Iraq.
1. Read The Bible In English And Hebrew:
2. Persian Gulf Oasis I:
3. Persian Gulf Oasis II:
4. Persian Gulf Oasis III:
5. Last Ice Age:
6. Glacial Retreat:
7. Cush = Kassites:
8. Wadi-Al-Rummah River: http://en.wikipedia.org/wiki/Wadi_al-Rummah