Eshnunna was an ancient Sumerian city and city-state in central Mesopotamia 12.6 miles northwest of Tell Agrab and 15 miles northw…Eshnunna was an ancient Sumerian city and city-state in central Mesopotamia 12.6 miles northwest of Tell Agrab and 15 miles northwest of Tell Ishchali. Although situated in the Diyala Valley northwest of Sumer proper, the city nonetheless belonged securely within the Sumerian cultural milieu. It is sometimes, in very early archaeological papers, called Ashnunnak or Tupliaš.