The mouth of the Arabian Gulf is the Straits of Hormuz. The northern side is Iranian - with the naval base at Badarabas, the southern side is Omani. Moving south from the along the coast you have Sharjah, Dubai, Doha then Qatar, Bahrain, Saudi Arabia and Kuwait.

Your eastern seaboard airbase supposes American aircraft would violate the airspace of sovereign countries. Historically they have never done this - example from recent history - the air attack on Lybia - permission to overfly was denied by France and Spain. Air attacks launched from Fairford in the UK had to fly down the Atlantic coast and into the Med through the Straits of Gibralter.