How easy is to travel from Dhahran?

Not a lot of direct flights beyond India, Pakistan, Philippines, Malaysia, etc and other Middle East destinations. For Europe there is a KLM to Amsterdam, and a couple of budget airlines that transit through Turkey. Also wizz air have a direct flight to Rome.

Lots of real options via Doha, Bahrain and UAE if you want choice.

It all depends on where you want to fly and how much you are prepared to spend.

For Europe Turkish and KLM are the best options for me at least to UK (KLM can be expensive at peak times or short notice and facilities / onboard services are really poor these days). Lufthansa can be ok price wise, but Frankfurt Airport is a pain due to having to clear security once landed and moving terminals.

Heading East you have Emirates, Qatar and Etihad which all offer extensive connections throughput Asia and the rest of the world as well as Pakistani and Indian carriers. Phillipine Airlines are ridiculously cheap for direct flights to Manilla also for example.

Africa options you can there are a couple - Egyptian and Ethiopia are the ones that spring to mind.

For the Americas a lot go via Europe, but you can fly to the US thru Emirates etc.

Also it is possible to get some really good offers thru the airlines if you subscribe to their mailing lists.

General prices to UK for my wife and daughter are 2,500-3,000 SAR as they can fly on random days and about 1k more for me as I tend to fly at busier times.