An international driving permit (IDP) is not a driving license, it is just a translation of the local driver's license, and based on the treaty (Convention on Road Traffic of 8 November 1968) you referred to, you can drive using it, but actually, you are driving using your local license, accompanied by the translation, which is called as the IDP. So, you have to understand that it is not a stand-alone document. The IDP in my hand right now even says "Issued according to Saudi Arabian Driving License No. so and so Valid Till so and so".
When I travelled in the past few summers to the UK, Cyprus, and Mauritius, I rented cars there using the IDP which I got from Jeddah. If I had been stopped in any of those countries there by the police, I would have showed them the IDP, but all the IDP is, is a translation of my Saudi license into English, and so it says I am allowed to drive in my home country, and by extension of the Convention, allowed to drive in the country I am visiting. The IDP is valid for one year only for categories of vehicles indicated in the license, and is valid in all 165 countries listed in the IDP. So, the convention was agreed upon to make things easy for travelers around the world. Imagine if every tourist or businessperson was required to get a local license before driving in a country they are visiting for a short time! So the convention basically says "To make it easy for everybody, yes, we will let you drive in a country you are visiting, but only based on your local home license, and to prove that you have a valid license in your home country, you have to get the IDP."
Sorry if you knew all that, but I just wanted to state all that because I have encountered many people over the years who think the IDP is a driving license and that anybody can get it from any country. You can get it only if you have a valid driving license in your country of residence, and as far as I know, you have to get it from your country of residence. So for example, when I traveled to Cyprus last year, I could not have just landed there and tried to get an IDP there, because to get get an IDP there, I would need to show a local, i.e., Cypriot license. If I had presented them with my Saudi license, they would have said "Sorry, we don't recognize this document and we have no way of knowing if it is real or not." Which mean, had I not got the IDP from Jeddah and traveled with it, I would not have been able to drive there.
So now, you are saying you want to get an IDP in Jeddah, based on your US license? As far as I know, that will not be possible. The IDP is given by the local automobile association (not really a 'business') in a given country. As you said, in the US it is the AAA, and here, it is the Saudi version, called as the Saudi Automobile and Touring Association (SATA). If you asked them to issue you an IDP based on your US license, they will give you the answer I gave in quotes in the previous paragraph. But, I hope I am wrong! Try it out.
As for where, I don't even know where SATA is located, neither do most people. Google can tell you, however, everybody here who gets an IDP before traveling gets it from any travel agency. They provide this service, by taking your documents and then handing them over to SATA who issue the IDP and give it back to the travel agency. The one I use, Caravan Travel, opposite the Saudi Airlines office inside Heraa Mall, charges 200. I am sure others charge the same. I have no idea how much is the actual IDP, and how much the travel agency charges for their service. If you can find a SATA office, go for it. You need to take a copy of your iqama, copy of Saudi driver's license, and 2 pictures. In your case, you don't have a Saudi driver's license, so take your US license. By the way, if you are going to be here for any reasonable amount of time, why not get the Saudi license?
