Currently reasonable accomodations are more or less limited to the Hotel Inter-Continental. While it doesn’t look bad, on-line booking is limited to an email query form on the Ariana Afghan Airlines website. Interestingly the Hotel Inter-Continental is not in any way related to InterContinental Hotels & Resorts.
The hotels aren’t part of the Sheraton hotel chain which is owned by Starwood Hotels and Resorts, and you won’t be collecting Starwood Preferred Guest points there.
It turns out that the properties were ITT Sheratons prior to the Gulf War. They continued to use the name even after economic relations were severed. There wasn’t much chance of the new Starwood corporate entity appealing to Saddam Hussein for damages.
Then again Pepsi continued to be sold in Iraq in the 1990s, even without involvement from Pepsico. Iraqis just didn’t get Brittany Spears as part of the package.
Update: Just this week Starwood Hotels & Resorts issued a statement distancing itself from the Baghdad Sheraton.