But with that slightly seedy side comes a vibrant cultural scene. Warehouses offer cheap rents for artists, dancers and musicians, and there are late-night hang-outs and music venues on and around Rue McGill St Laurent including the quirky Casa del Popolo, Sala Rossa, Divan Orange and Club-Soda.
If you're lucky, you might spot the singer tucking into his favourite smoked beef sandwich in Main, across the road from the more famous Schwartz's, which has just been bought by another well-known Canadian, Celine Dion.
In October 2016, the former Sky worker was found by her horrified flatmate with her throat slashed in their Gateshead home, after months of being stalked and harassed by her ex-boyfriend Lance Corporal Trimaan 'Harry' Dhillon.
No one has a bad word to say about the gentlemanly ladies' man, but locals don't go out of their way to celebrate the 78-year-old singer, whose renaissance and epic world tour in the past five years has made him a star once more.
However, Allen was left to rue a missed black off its spot when it seemed he was going to close out the match with the score at 5-4. Gilbert knocked in breaks of 88, 68 and then 63 in the final frame to triumph 6-5.
There are quirky shops and restaurants and an artists' quarter has been redeveloped. The port, where Suzanne lived, is now a leisure centre with bike tracks, cafes, an Imax cinema and even a new sandy beach, based on Paris Plages, the Seine beaches.
But, with some detective work and lots of walking, it's possible to piece together his life in the French Canadian island city of under two million souls. Dunn's Birdland jazz club, on St Catherine Street, where he made some of his first appearances as a singer, is no more.
However, finding landmarks associated with Cohen - who wrote the much-covered hit Hallelujah, and was born and raised in the city - isn't easy. The statue of Our Lady of the Harbour still towers above the 17th-century La Chapelle de Bon-Secours.
He later enrolled at McGill, created by Scotsmen from Scottish stone and the country's equivalent of Oxbridge. At night, a young Cohen would sneak out to visit St Catherine Street - now the main shopping thoroughfare - to the lively music joints.
It is edgy in areas, with a high number of girly bars in the centre. The papers are full of a corruption scandal, which shows the Mafia is still at work here. There is more than a whiff of Seventies' New York about the major city of the Quebec province.
The city is host to the world's largest jazz festival every summer, and in the jazz hall of fame building on St Catherine there's a small tribute to Cohen with one of his famous, trademark hats displayed against a distinguished picture of the great man himself.
For a musical legacy with a difference, guests at the Fairmont Queen Elizabeth, just below McGill, can stay in suite 1742, where John Lennon and Yoko Ono staged one of their famous anti-war bed-ins in 1969, recording their famous song Give Peace A Chance in the room.