I don't want to overwhelm anyone with information (this isn't going to be a history lesson, I've tied to simplify as much as I can) but here's an idea of the fragmented nature of the kingdoms at the time.
-Important city-states/kingdoms in 1767 BCE-
Mesopotamia:
Babylon — Hammu-rapi reigns in Babylon. His influence extends to several of those cities nearest him, in the region of the middle Euphrates River. The oldest of these cities is Kiš, followed by Sippar. Babylon and nearby Borsippa (OB. Barsip) are less than a half a millennia old. The inhabitants of the Babylonian city-states are primarily ethnic Akkadians, though a powerful Amorite minority resides there as well.
Larsa - Rim-Sin, the king of Larsa, controls the city-states of southern Mesopotamia. These include ancient Sumerian cultural centers that have existed since the dawn of written history. In addition to Larsa, these cities include Bad-tibira, Eridu, Isin, Lagaš, Larsa, Nippur (OB. Nipuru), Umma, Ur (OB. Urim), and Uruk. The population of Larsa is thoroughly Akkadian, those Amorites and Elamites are significant minorities.
Mari - Ten years ago, the city-state of Mari was part of Assyria, governed by no less than Yašmah-Adad, the second son of the great king Šamši-Adad. But soon after the death of Šamši-Adad in 1776 BCE, an Amorite chieftain named Zimri-Lim deposed the Assyrian prince and set up Mari as an independent entity. As a result of its position on the trade route along the middle Euphrates, Mari was already a large and important commercial center. By 1767 BCE, Zimri-Lim’s control extends to several cities in the region along the Euphrates and Habur rivers, including Hit, the capital Mari, Qattunān, Saggaratum, Terqa and Tuttul. While many ethnic Akkadians remain in the Mariote cities, the populace is now majority Amorite.
Assyria - Assyria (or the Kingdom of Upper Mesopotamia) is a flagging power, still recovering from the loss of its great king Šamši-Adad several years before. At that time, Assyrian puppets controlled the cities in an area from the Zagros Mountains to the western bounds of Mari on the Middle Euphrates. The power and influence of Išme-Dagan (I), the current Assyrian king, extends from Aššur to the city-states of Nineveh (OB. Ninuwa) and Razama. The people of these cities remain Akkadian for the most part, but as in Babylon and the Larsan territories, an Amorite minority is growing.
Ešnunna - Centered on the banks of the middle Tigris, Ešnunna is surrounded by powerful kingdoms, with Assyria to its north, Babylonia and the Larsan cities to its south, and the aggressive nation of Elam to its east. In addition to the capital Ešnunna, King Ibal-pi-El (II)’s influence extends to Tutub. Ešnunna’s people are ethnically Akkadian, although Elamites and Amorites are appreciable minorities.
Border Kingdoms:
Andariq - In the vacuum left by the decline of Assyria after the death of Šamši-Adad, the northern city-state of Andariq (or Andarik) has carved out a small sphere of influence along the northern reaches of the Habur River. Its current king, Qarni-Lim, maintains close ties to the king of Mari; many see him as a virtual puppet ruler. From Andariq, Qarni-Lim’s fragile rule extends to the cities of Kurda and Šubat-Enlil. While a bare majority of the citizens of Andariq are Akkadian, given its northerly position, many other prominent minorities exist, including the ubiquitous Amorites, but also new arrivals from Asia Minor, including the Hurrians.
Yamhad - Along with Qaṭna, the kingdom of Yamhad is one of two great western powers. Centered on Ḥalab, the King of Yamhad, Yarim-Lim (I) controls the northern trade routes to the Mediterranean. As a result, Yamhad is a powerful nation, one that often meddles in the affairs of the smaller kingdoms of Mesopotamia. This loose confederation of city-states includes Halab, as well as Alalah, Ebla and Ugarit (OB. Ugaritum). The people of Yamhad are heavily Amorite during this time period, although a sizable minority among the northern city-states are Hurrian.
Qaṭna - Like its rival Yamhad, Qaṭna (OB. Qaṭanum) is a region to the west of Mesopotamia, reaching as far as the shores of the Mediterranean. In 1767 BCE it is powerful enough to influence Mesopotamian matters of state. In addition to the city of Qaṭna, this kingdom includes the ancient site of Tadmir (modern Palmyra). Like the people of Yamhad, Amorites are the overwhelming majority in Qaṭna.
Elam - Situated in the mountainous regions on the eastern edge of Mesopotamia, Elam is an ancient., powerful kingdom that often mettles in Mesopotamian affairs. Currently ruled by the sukkalmahhum Siwe-palar-huppak from Susa, Elam also includes the city of Anšan. The people of Anšan are Elamite, with few exceptions. Susa has a substantial Akkadian population. Elam, with its distinctive language and culture, is less likely to assimilate other peoples.
My idea is to start with everyone based in Babylon. The PCs will probably need a fairly solid connection to that city, even if they're from somewhere else.
Edit:
Here's a map.
