So, yesterday I was a story from the one thousand and one Arabian nights book, and I noticed that after each mention of the city of Damascus; the author likes to remind the reader that Damascus is infamous for homosexuality, corruption, and decadence.
Is there any historical evidence to such a claim?
Well, no one has given this an answer so I'll just make one note for you.
I'm not familiar with the particular background of that particular passage in the thousand and one nights (or even if it comes from one of the European additions to the text!)
However what I can point out is that Damascus was the capital of the Umayyad caliphate. The "Nights" stories in theory date back to the reign of the Abbasids, most famously Harun al-Rashid (although as I said, many of the European editions contain additional stories that were added in the 18th and 19th centuries.)
Abbasid propaganda more or less accused the Umayyads of the same decadences you've ascribed to their capital of Damascus. In contrast with the Rashidun caliphs and the Abbasids themselves the Ummayads were said to have practiced "Mulk" or Earthly Kingship rather a righteous Caliphal authority.
Of course, the Abbasid court itself was quite obviously decadent with the poetry of men like Abu Nuwas, who features in the "Nights" practically brimming with poems of drinking, pederasty, and other decadent acts.
Nonetheless the decadence of the Umayyads was a standard feature of their portrayal in Abbasid literature.
Damascus was the capital of the Umayyad caliphate: following their defeat by the Abbasid dynasty, a new capital was established at Baghdad (and essentially built up from the ground). The latter city was the location of the 1001 Arabian nights, and many of its tales are set there: as a work composed under the Abbasid dynasty, it is unsurprising that, for political expediency, this former and supplanted capital would be decried: implicit in its existence it embodied the vices of the Umayyads that the Abbasids sought to decry.