Described as "the best damn whorehouse in the Capital Wasteland. Strong booze and soft women." It was shut down in the summer of '49 (presumably 2249, since the game occurs in 2277) when most of the ladies died of a Cholera Outbreak." The proprietor was a Madame by the name of Destiny Chao (also mentioned in Dashwood's computer), who also died in the outbreak.
Blue Destiny Brothel is mentioned only in Fallout 3.