I thank you for asking the question of "Where were Abraham living in Genesis 18?" I will do some searching for information that will help you know where he lived at this time.

The first bit of information comes from the King James Version of the Bible. The verse is verse #1 and it says Abraham lived on the plains of Mamre. There is the information source:

http://www.biblegateway.com/passage/?search=Genesis+18&version=KJV

The second set of information comes from the New International Version of the Bible. On verse #1 it tells us that Abraham lived near the great trees of Mamre. Here is the link:

http://www.biblegateway.com/passage/?search=Genesis+18&version=NIV

When looking up the place of Mamre, it shows that Mamre is in the land of Canaan.

http://www.biblegateway.com/keyword/?search=Mamre&version1=31&searchtype=all

I searched in the keyword section for Mamre and found the place where Mamre is. Here is a verse from Genesis that tells us where Mamre is.

Genesis 23:19 Afterward Abraham buried his wife Sarah in the cave in the field of Machpelah near Mamre (which is at Hebron) in the land of Canaan.

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