What does the Bible tell us about Abraham? Genesis 11:28 says that Abraham’s father, Terah, lived in Ur, an influential city in southern Mesopotamia situated on the Euphrates River about halfway between the head of the Persian Gulf and the modern-day city of Baghdad. Terah took his family and set off for the land of Canaan but instead settled in the city of Haran in northern Mesopotamia (on the trade route from ancient Babylonia about halfway between Nineveh and Damascus). The people of Ur and Haran worshiped the ancient Babylonian pantheon of gods, in particular the moon god, Sin. God then calls Abraham out from his home in Haran and tells him to go to a land that He will show to him.
Much later God commands Abraham to sacrifice Isaac on the top of Mount Moriah:
“Take your son, your only son Isaac, whom you love, and go to the land of Moriah, and offer him there as a burnt offering on one of the mountains of which I shall tell you” (Genesis 22:2).
There, Abraham builds an altar to make the sacrifice, but God’s angel stays Abraham’s hand. Instead, God provides a ram as a sacrifice:
“And Abraham lifted up his eyes and looked, and behold, behind him was a ram, caught in a thicket by his horns. And Abraham went and took the ram and offered it up as a burnt offering instead of his son. So Abraham called the name of that place, “The Lord will provide”; as it is said to this day, “On the mount of the Lord it shall be provided” (Genesis 22:13-14).
The name Moriah is explained in 2 Chronicles 3:1 as the place of the later Temple Mount in Jerusalem:
“So Solomon began to build the Temple of the Lord in Jerusalem on Mount Moriah, where the Lord had appeared to David, his father. The Temple was built on the threshing floor of Araunah (or Ornan in Hebrew) the Jebusite, the site that David had selected.”
The ESV Study Bible makes this comment:
“Abraham bound Isaac in the land of Moriah and tradition associated the Temple mount as the place where the Lord provided for Abraham.”
Genesis 21:14-29 describes how Abraham sent Hagar and Ishmael out into the desert and how God intervened to provide water for them. Ishmael grows up in the wilderness and becomes a skillful archer. He settled in the wilderness of Paran and then married a woman from the land of Egypt.
“About this time” Abraham lays claim to a well he dug in Beersheba (which means “well of the oath”). “Abraham planted a tamarisk tree at Beersheba, and there he worshipped the Lord, the Eternal God” (Genesis 21:32-34).
There is no reference here to Abraham building a house for worship, and Beersheba is clearly nowhere near Mecca. The only connection between Abraham and a house of worship is the place on Mount Moriah where he was prepared to sacrifice Isaac – the place where Solomon eventually built the Temple. That location is in Jerusalem.
EDIT: Just found a reference to Baca in Psalm 84:6 (Authorised Version): "Who passing through the valley of Baca make it a well; the rain also filleth the pools." That is in the context of people struggling to travel to Zion to worship God in Jerusalem. Many other Bible translations call it the valley of Weeping. I don’t know if this is the same as the Bakkah mentioned in the question, but it certainly has nothing to do with Mecca.