It depends what you mean by "city-state". If you are referring to Emirates (Arab Tribal Principalities), then the largest in area is Kuwait, which sits on the Persian Gulf.
If you are talking about historic city-states, there are several historic city-states in the Mesopotamian valley, like Akkad or Sumer. Additionally, as the Persian Gulf lies between modern day Saudi Arabia and Iran, the closest Ancient Greek city-state would have been Knossos, where the Mycenaean Greeks lived.
There are actually several small countries (which are small enough to qualify as city-states) located directly IN the Persian Gulf:
Qatar
The first is probably the best fit for a definition of both "city-state", and "closest to", being that it is barely 750 sq km in size, and effectively is an island archipelago off the shore of Saudi Arabia.
The Persian Gulf.
That is Iran
Arabian peninsula
Not in, but the UAE borders the Arabian (or Persian) Gulf which is a shallow sea
The Persian Gulf :)
Persia, today called Iran.
Persian Gulf.
Persian Gulf.
That is the Arabian Peninsula.
The body of water separating Iran from Saudi Arabia is called the Persian Gulf. There has been a push by the Arabs to have the Gulf renamed the Arab Gulf (as it is called "al-Khalij al-3arabi" in Arabic). No non-Arab nation has adopted this nomenclature.
The State of Kuwait is on the northwestern shore of the Persian Gulf. Kuwait is located in the northeastern part of the Arabian Peninsula. Kuwait consists of the mainland on the peninsula as well as nine nearby islands.
There is no such thing as the "Chadian Sea".