re: Has anyone been to Amman, Jordan?

Never been to Jordan but been in other parts of the region.

From a crime standpoint, I would imagine it’s quite safe, the only thing that could be worse compared to the US would probably be pickpocketing of a female tourist who is not accompanied by a man.

I would certainly not recommend your cousin to get drunk in public and nothing is going to have the atmosphere of an SEC bar but a few drinks at a hotel bar is certainly acceptable and the cops aren’t looking to target buzzed/non-disruptive but slightly drunk tourists.