عين (ayn) is "eye", "spring", or a host of other meanings, depending upon precise context. I believe that Sukhmah is not an Arabic word. Where is this city? Perhaps the word is Persian, Hindi, Berber, or some other language..?
As you have learned, "al" means "the". "Adibiyah" will have slightly different translations depending upon precise spelling. I am assuming that the Arabic word you are romanizing (writing with the English alphabet) is الادبيه, which translates roughly as "morality", "humanities", or "culture". The root word is ادب, which is a verb meaning "to be well-bred, well-mannered, cultured, or urbane". الادبيه are the things which make a person able to be well-bred, well-mannered, cultured, and/or urbane.
Cheers!