Where can I find information about post-WW2 airports in Saudi Arabia?
There have always been three primary airports, representing the commercial hubs of Saudi Arabia:


Dhahran International Airport / Dammam - King Fahad International Airport


This was a dual use, single runway airfield which was the primary international commercial airport for the Eastern province, until the new Dammam International was commissioned and opened for the first flight in November 1999; Dhahran has since been reverted back to military use and is still actively being used today.


Riyadh Airport / King Khalid International


As with Dhahran - Riyadh Airport is a military dual-use airport until the dedicated King Khalid was opened in 1982, and the old Riyadh airport (OERY) was reverted back to military use.


Jeddah Airport / King Abdulaziz International


This is busiest airport in the kingdom, also one of the largest terminal buildings in the world. It is also the hub of the state carrier Saudia. It opened for service in 1981.

There then the secondary airports which also service international flights:


Medina / Prince Mohammad Bin Abdulaziz International (OEMA) - Opened in 1950; new terminal opened in 2015. 
Taif International - Opened in 1976, it gained importance as it is the closest airport to Makkah (the Holy City) - and it is one of the most popular summer destinations in Saudi Arabia.


There are a lot more regional and domestic airports is Saudi Arabia. You can find information on those from the General Authority for Civil Aviation (GACA) website.

Saudia (the flag carrier) has great information dating back to 1945 available on their website.

King Abdulaziz: His Plane and His Pilot is a great book that covers the history of Saudi aviation.