Ashur (aka Assur or Asur) is on the west bank of the Tigris, north of where it is joined by the Lesser Zab. Today, it is modern قلعة شرقاط, meaning Castle Sherqat and commonly transliterated as Kaleh-Shergat or Qala't Shargat.
When looking at artifacts, a winged sun-disk (sometimes containing a homunculus) represents Ashur. Excavations began by Germans under W. Andrea's leadership in 1913-1914.
whc.unesco.org (great article from when Ashur was nominated to be a world heritage site