[ichabod1]

Baghdad is said to have been founded in A.D. 762, so it didn't exist yet in the days of Caesar or Trajan. Caesar never got that far east, but Trajan's last campaign was in Mesopotamia shortly before his death.

I believe it would have been Babylon at that time, what, 25-50 miles from Baghdad?

[Verginius Rufus]

Baghdad is about 50 or 60 miles from the ruins of Babylon (just estimating it from the map). A closer city to the modern Baghdad was Seleucia on the Tigris, founded by Seleucus I about 312 B.C., but destroyed in A.D. 164 (earlier burnt by Trajan). The Parthians built a city on the other side of the river near Seleucia, known as Ctesiphon, which became the capital of Babylonia after the destruction of Seleucia, and which was later the capital of the Sassanian Persian empire (3rd century to 7th century).