Gen 11:31 Terah took Abram his son and Lot the son of Haran, his grandson, and Sarai his daughter-in-law, his son Abram's wife, and they went forth together from Ur of the Chaldeans ( Ur [Light] of the ones of Kesad [Clod breaker] ) to go into the land of Canaan, but when they came to Haran, they settled there. (ESV)

Where was Abraham's Ur?

Gen 11:31 Terah took Abram his son and Lot the son of Haran, his grandson, and Sarai his daughter-in-law, his son Abram's wife, and they went forth together from Ur of the Chaldeans ( Ur [Light] of the ones of Kesad [Clod breaker] ) to go into the land of Canaan, but when they came to Haran, they settled there. (ESV)

Abraham was from the city of Ur according to Genesis 11:31 above. The problem is that there are several places called Ur. It is mostly translated as "Ur of the Chaldeans."
The problem with "Chaldeans" is that it is a late word used in the Neo-Babylonian times. It is either anachronistic, or a poor translation.
Josephus and Rabbi Maimonides believed that Ur Kasdim was in Northern Mesopotamia, in what is today Syria or Turkey.
There is no debate over where Haran is located, 10 miles north of the Syrian border in Turkey along the Balikh River, a tributary of the Euphrates River. Haran is an important Hurrian center, mentioned in the Nuzi tablets. The moon god, Sin was worshiped here.
There are two cities not far from Haran; Ura and Urfa. Local tradition says that Abraham was born in Urfa. Northern Ur is mentioned in tablets at Ugarit, Nuzi, and Ebla, which refers to Ur, URA, and Urau (See BAR January 2000, page 16).
The names of several of Abraham's relatives like Peleg, Serug, Nahor and Terah, appear as names of cities in the region of Haran (Harper's Bible Dictionary, page 373). Abraham sent his servant back to the region of Haran to find a wife for Isaac (Genesis 24:10).

Gen 24:4 You must go back to the country where I was born (nativity) and get a wife for my son Isaac from among my relatives."
Gen 24:10 The servant, who was in charge of Abraham's property, took ten of his master's camels and went to the city where Nahor had lived in northern Mesopotamia (Aram Naharaim) . (GNB)

After working for Laban, Jacob fled across the Euphrates River back to Canaan (Genesis 31:21). If Ur were the one in Southern Mesopotamia, then Jacob would not need to cross the Euphrates. Laban is said to live in Paddan-Aram, which is in the region of Haran (Genesis 28:5-7), which seems to be the same area as Aram-Naharaim, Abraham's homeland (Genesis 24:10).
All this evidence taken together seems to indicate that the Ur of Abraham was in the same region as Haran in Northern Mesopotamia, and NOT the famous Ur in Southern Mesopotamia.
There are two ancient tribes to which the Hebrew word translated as Chaldeans may refer to, the Kaldu or the Kassites.
from: http://en.wikipedia.org/wiki/Chaldea
"The homeland of the Semitic Chaldean people ( Kaldu ) was in the far south east of Mesopotamia. It is not certain when they migrated at an unknown period into the country of the Mesopotamian sea-lands about the head of the Persian Gulf. They seem to have appeared there at about the same time that other new Semitic peoples, the Arameans and the Sutu appeared in Babylonia, circa 1000 BC. This was a period of weakness in Babylonia, and its ineffectual kings were unable to prevent new waves of peoples invading and settling in the land.
Though belonging to the same Semetic ethnic group, they are to be differentiated from the Aramean stock; and the Assyrian king Sennacherib, for example, is careful in his inscriptions to distinguish them. When they came to possess the whole of southern Mesopotamia, the name "Chaldean" became synonymous with "Babylonian", particularly to the Greeks and Jews."
from: http://en.wikipedia.org/wiki/Kassites
"The Kassites were an ancient Near Eastern people who gained control of Babylonia after the fall of the Old Babylonian Empire after ca. 1531 BC to ca. 1155 BC (short chronology). Their Kassite language is thought to have been related to Hurrian, and not Indo-European or Semitic although the evidence for its genetic affiliation is meager due to the scarcity of extant texts.
The original homeland of the Kassites is not well known, but appears to have been located in the Zargos Mountains in Lorestan in what is now modern Iran, although, like the Elamites, Gutians and Manneans, they were unrelated to the later Indo-European/Iranic Medes and Persians who came to dominate the region a thousand years later. They first appeared in the annals of history in the 18th century BC when they attacked Babylonia in the 9th year of the reign of Samsu-iluna (reigned ca. 1749–1712 BC), the son of Hammurabi. Samsu-iluna repelled them, as did Abi-Eshuh, but they subsequently gained control of Babylonia circa 1570 BC some 25 years after the fall of Babylon to the Hittites in ca. 1595 BC, and went on to conquer the southern part of Mesopotamia, roughly corresponding to ancient Sumer and known as the Dynasty of the Sealand by ca. 1460 BC. The Hittites had carried off the idol of the god Marduk, but the Kassite rulers regained possession, returned Marduk to Babylon, and made him the equal of the Kassite Shuqamuna. The circumstances of their rise to power are unknown, due to a lack of documentation from this so-called "Dark Age" period of widespread dislocation. No inscription or document in the Kassite language has been preserved, an absence that cannot be purely accidental, suggesting a severe regression of literacy in official circles. Babylon under Kassite rulers, who renamed the city Karanduniash, re-emerged as a political and military power in Mesopotamia. A newly built capital city Dur-Kurigalzu was named in honour of Kurigalzu I (ca. early 14th century BC)."
Thus assuming that the Hebrew kasddim were either the Kassites of the Late Bronze Age or the Kaldu of Iron Age Mesopotamia, it would seem useful to look for a location of these peoples prior to their movement into southern Mesopotamia.
The Kassites moved into Babylon sometime after the sacking of that city by the Hittites in 1595 B.C. Immediately before occupying Mesopotamia they might have been in the upper Euphrates River valley around the confluence of the Habur and the Euphrates. Most Assyriologists maintain that before moving into southern Mesopotamia the Kassites entered the Euphrates River valley from the north, probably from somewhere in Asia Minor, where they may have been for several centuries before moving south. This would place the Kassites, one of the possibilities for the Hebrew kasddim, somewhere north of Mesopotamia at the time of Abraham, definitely a long distance from the Uri(m) of southern Mesopotamia.
The other possibility for the kasddim, the Kaldu, are first mentioned in the ninth century B.C. If they are Arameans or related to the Arameans, and this is not certain, we may seek their origin in northern Syria and southeastern Turkey where the oldest Aramaic inscriptions, none of which predate the first millennium, have been found. Again, in the case of the Arameans, the Ur of the Chaldeans cannot be located in southern Mesopotamia but must be sought in an area comprising present-day Syria, Lebanon and the southeastern parts of Turkey bordering Syria.
Conclusion
There are compelling reasons to place Ur of the Chaldees near Haran. And may be either Ura or Urfa, with Urfa being the traditional location. From Wikipedia article on Urfa "According to Turkish Muslim traditions Urfa (its name since Byzantine days) is the biblical city of Ur of the Chaldees, due to its proximity to the biblical village of Hurran. Urfa is also known as the birthplace of Job."

 ( see photos of The Great Mosque and Abraham's Cave in Sanliurfa.)