In May 2015 we went to Berlin and I finally got to the Pergamon Museum - a grand old institute based on the old discover-and-plunder school of archaelogy.
Which means that if you want to see the Ishtar Gate of ancient Babylon (and I did), you go to Berlin and not Iraq.
It worked well for me, as I doubt Iraq will settle down enough to be a tourist destination in my lifetime. Adorning the walls of Babylon were lions and mušḫuššu, which Wikipedia describes as a mythological hybrid: a scaly dragon with hind legs resembling the talons of an eagle, feline forelegs, a long neck and tail, a horned head, a snake-like tongue, and a crest. Luckily the gift shop also had mušḫuššu, so I now have one in my “kitsch cabinet” of souvenirs.
Another exemplar captured alive for my kitsch cabinet.