Two things at Ur are worth more attention than the ziggurat, and they pull in opposite directions.
Enheduanna was installed by her father Sargon of Akkad as entu, high priestess of the moon god Nanna at Ur, in the twenty-third century BC. Compositions attributed to her survive, above all the Exaltation of Inanna, and they name her, describe her circumstances, and speak in the first person about being driven from office and restored. That makes her the earliest author anywhere whose name is attached to their work. The attribution is not entirely uncontested: the surviving copies are school texts written down some centuries after her lifetime, and a minority of Assyriologists treat the authorial voice as a later literary construction. The majority position accepts her as a historical author, and either way the texts show that a woman at the head of a major cult was a figure whose name was worth attaching to poetry.
The office itself is the interesting political fact. Sargon conquered Sumer and then installed his daughter as the priestess of its principal moon cult, which fused Akkadian power to Sumerian legitimacy without abolishing either. Later kings copied the arrangement for centuries.
The Royal Cemetery is the other thing, and it is grimmer. Woolley excavated some two thousand graves in the 1920s, and among them sixteen he called royal, in which a principal burial was accompanied by attendants: soldiers at the entrance, grooms with oxen and carts, and rows of women in elaborate headdresses of gold, carnelian and lapis. In the largest, dozens died together. Woolley reconstructed a scene in which they walked down voluntarily and took poison from cups found beside them.
That reconstruction has been revised. CT scanning of skulls from the cemetery, published in 2009, found evidence of blunt force trauma to the head, indicating that at least some of the attendants were killed by a blow rather than drugged, and that bodies were heated and treated with mercury to preserve them during the ceremony. The rite was longer, more managed, and more violent than Woolley described. What it meant to those who died in it is not recoverable.
The finds were divided between London, Philadelphia and Baghdad under the partage system, which is why the objects that define Sumerian art for most people (the Ram in a Thicket, the Standard of Ur, the lyres), are in three countries and none of them is Iraq alone.