The scholarly community is divided as to where these ancient rivers and countries are located. The following answer presents one view:

There are more than one land of Havilah and of Cush respectively mentioned in the Bible, wherein lies the confusion.  However, the verses in Genesis cited above give us a clue as to which area is delineated.  The garden of Eden, it is generally accepted, was located in the Armenia/Azerbaijan region, located in the Republic of Georgia, i.e.,the Caucasus Mountains,  north eastern Turkey and north west Iran.  The word Cush means blackness.  The black races generally inhabit southern Iraq, south India and Africa.  But Nimrod was also black, being a Cushite, and he built the city of Babel, or the city of Cush, in what is today northern Iraq.  Hence the land of Cush, translated Ethiopia in verse 13, cannot refer to Ethiopia in north east Africa, also black, but to Northern Iraq in Asia, within what was later the Assyrian empire .  Furthermore, verse 11 mentions that there is “good gold” in the area of Havilah.  The second-largest gold deposits in the world are found near the delta of the southeast Caucasus Mountain range (the first being in South Africa, far from Eden).  We can then be assured that the Bible is speaking of this region in what is the general area of the Republic of Georgia.

Since the world experienced a devastating flood which destroyed a good part of the land geography, some scholars believe it is impossible now to determine exactly which today are the four rivers mentioned in Genesis, as their source has been obliterated.  Many agree the river Hiddekel is the Tigris river that empties into the Persian Gulf and the Euphrates has a similar starting point.  A discerning look at a map of the area will reveal that the Pishon is likely the Araxes or Araks river, that “compasseth the  land of Havilah,” the gold mines in the area of the Republic of Georgia, and empties into the Caspian Sea.  A closer look may suggest that the Gihon river which “compasseth the …land of Ethiopia

[Cush],” Northern Iraq and Northwest Iran, may be the Safid-Rud river, which also empties into the Caspian Sea.  It may be noted that the history of Adam and the human race parallels that of the river that arose in Eden.

The other view may be read under the question: Where is the location of Eden in our present world?