Unfortunately, KSA is the only GCC country who doesn't accept GCC residents for visits (visa on arrival). The only way to visit Dammam is to get a drive-through visa to Bahrain. First you have to get a visit vist to Bahrain (which is done in 2 hours, they are very professional) and the other visa to Saudi which takes at least 4 days through a service agent (u r not allowed to deal with the Saudi embassy, don't know why)

Remember, u have to drive to Bahrain otherwise u will have to pay a fine when u exit from Saudi, and Bahrain is a nice place to visit and it's only 30 minutes from Khobar.

Have a nice trip and drive safely