“Then his sons Isaac and Ishmael buried him in the cave of Machpelah, in the field of Ephron the son of Zohar the Hittite, facing Mamre, the field which Abraham purchased from the sons of Heth; there Abraham was buried with Sarah his wife. It came about after the death of Abraham, that God blessed his son Isaac; and Isaac lived by Beer-lahai-roi. ” Gen. 25:9-11
We should note that, at least in Abraham’s death, Isaac and Ishmael were present together. Ishmael and Hagar were sent away by Sarah, with God’s approval, in Genesis 21 while Isaac was still young. Isaac would be 75 years old at this point – the same age Abraham was when he heard God’s calling (Gen. 12:4).
Everett Fox in his commentary notes that Isaac receives his blessing directly from God, unlike Jacob and Joseph who receive the blessings from their fathers.
The place Isaac chose to live, Beer-lahai-roi, was the place where Hagar encountered God for the first time after fleeing from Sarah (Gen. 16:14). Beer-lahai-roi is typically translated as “The Well of the Living One who sees me.” For some additional etymology on this place name, please see http://www.abarim-publications.com/Meaning/Beer.html
For more information on the Cave of Machpelah where Abraham and Sarah are buried, please see my previous postings on Genesis 23 here.