There was a time before things started to get cleaned up in the 90s, when it looked likely - Chicago was the city of the future in the US in the 70s and 80s, while New York was a trashy, depressed place with porn shops in Times Square. Watch Taxi Driver or the Warriors - New York was once a place any tourist or hipster would have feared to tread.
This. obviously wall-street and the surrounding important areas could remain strong, but the rest of the city falls into a spiral. I'm not sure you can make it Detroit level bad as it is located ina very strategic location and not sole dependent on "A industry" for survival.
That said, during the 70's and 80's along with Chicago, Dallas, Austin, San Francisco, LA and even DC/Northern Virginia were quite attractive markets for companies.
NYC could look more like Newark/Bronx, if not for the drastic measures taken to clean the core city up. However Detroit level bad? that would take a level of sheer incompetence that would be historic in nature.
Detroit's major problem was white flight to suburbs and shady real-estate practices during the 60's and 70's, and the Detroit Riots and miles upon miles of suburb's for them to run too. Auburn Hills is a suburb for all intensive purposes, any further north and you run into Flint Suburb's. obviously many people moved out of the NYC to Connecticut, upstate, and NJ or out to Staten island, but the cost of living kept rising in these suburbs due to fact that people wanted a plot of grass in their own little worlds.
I guess one way that could do it, have the Harlem Riots be worse and spread in the city itself, have them continued in 68 on the same level as other cities. no world trade center, leaving Radio row intact. (The WTC complex spurred a fair amount of urban retooling.) Have more large financial organizations flee to say Chicago or disperse around the nation.
I don't see it ever being E. St Louis or Detroit level bad, but you could put a dent in things.