Arabia was a region of Earth, inhabited by Arabs. It was located in the Middle East, a region of Western Asia. The Arabian Sea lapped at the southern coastline of this peninsula.
In a mid-20th century mystery novel read by Data in 2364, the lead character, Doctor John Rawley thought, but didn't say, that the perfumes of Arabia would be unable to soften the features of Frederricka Wilson. (TNG: "The Big Goodbye")
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The Arabian peninsula was also mentioned in a deleted scene from Star Trek Generations; Kirk started his orbital skydiving trajectory by jumping out over the peninsula. [1]
Retroactive continuity: The location of the Arabian Peninsula was depicted on a statistical map. The map was stored in the library computer of the USS Enterprise. This map was assimilated by the Talosians in their study of Humans in 2266. (TOS: "The Cage")
The Arabian city of Mecca would appear to be the namesake of New Mecca. Arabia is also the region originating Islam.