Its a story, nicked from the Babylonians. But if you are silly enough to think that it was an actual place, then you must also swallow the other story that talks about a big flood, also nicked from the Babylonians, which would have swept it away.
The Bible has a nice little trick of destroying the evidence of any 'fact' it creates to tell a story a few lines later, so nobody can question the 'fact'
The origin of the term "Eden", which in Hebrew means "delight", may lie with the Akkadian word edinu, which itself derives from the Sumerian term E.DIN - arid steppe land (west of the Euphrates.)
The Book of Jubilees, canonical to this day in the Ethiopian Orthodox Church, relates a tradition that the angels did not place Adam in the garden until his 40th day, and his wife Eve on the 80th day. Later on (4:23-27), it states that they also conducted Enoch into the garden of Eden when he was translated from the Earth at age 365, where he records the evil deeds of mankind for all time — adding further that the garden is one of four holy places that the Lord has on Earth, the other three being Mount Sinai, Mount Zion, and the 'Mount of the East' (usually assumed by scholars to mean Mount Ararat).
Most put the Garden somewhere in the Middle East near Armenia, with Jewish tradition citing Yerevan at 40°10′12.0″N, 44°31′12.0″E, and with Mount Ararat only 30 miles to the south west. Some theologians have claimed that the Garden never had a terrestrial existence, but was instead an adjunct to heaven as it became identified with Paradise.
The text asserts that the Garden was planted in the eastern part of the region known as Eden, and that in Eden, the river divided into four branches: Hiddekel (also known as Tigris), Euphrates, Pishon and Gihon. While the identity of the first two is commonly accepted, the latter two rivers have been the subject of much debate. If the Garden of Eden had been near the sources of the Tigris and the Euphrates, then the narrative might have identified it as located in the Taurus Mountains, or in Anatolia, specifically the Armenian Highland in eastern Turkey.
In Assyrian records, there is mention of a "Beth Eden", (House of Eden), a small Aramaean state, located on the bend of the Euphrates River just south of Carchemish, in the vicinity of Urfa and Harran (Turkey). This is located approximately 430 miles south west of Yerevan at 36°55′N, 38°00′E.
Satellite photos reveal two dry riverbeds flowing toward the Persian Gulf near where the Tigris and Euphrates also terminate. This would account for four easterly flowing rivers. Archaeologist Juris Zarins claimed that the Garden of Eden was situated at the head of the Persian Gulf, where the Tigris and Euphrates Rivers run into the sea at 29°47′0″N, 48°38′0″E, from his research on this area using information from many different sources, including Landsat images from space. In this theory, the Bible’s Gihon River would correspond with the Karun River in Iran, and the Pishon River would correspond to the Wadi Al-Batin river system (also now called the Kuwait River) that 2,500-3000 years ago drained the now dry, but once quite fertile central part of the Arabian Peninsula from the Hijaz mountains 600 miles to the South West. This theory is supported by C. A. Salabach
Some of the historians working from within the cultural horizons of southernmost Sumer, where the earliest surviving non-Biblical source of the legend lies, point to the quite genuine Bronze Age entrepôt of the island Dilmun (now Bahrain) in the Persian Gulf, described as 'the place where the sun rises' and 'the Land of the Living'. The setting of the Babylonian creation myth, Enûma Elish, has clear parallels with the Genesis narratives. After its actual decline, beginning about 1500 BC, Dilmun developed such a reputation as a long-lost garden of exotic perfections that it may have influenced the story of the Garden of Eden. Some interpreters have tried to establish an Edenic garden at the trading-center of Dilmun.
There is also a Sumerian story about a mountainous kingdom accessible from Sumer by river called Aratta.
but in all honesty, you might as well just choose the place that suits your own view-point?