Fists of Fury: Novigrad - Novigrad
Quest Giver: Novigrad Notice Boards or Master Claytop
Other Requirements: N/A
You can start this quest one of two ways; the first of which is by grabbing it off almost any of the Novigrad Notice Boards throughout the city and the second way is by speaking with Master Claytop inside of The Golden Sturgeon.
This is the second fist fighting quest that you'll get in Witcher 3, with the first one being Fists of Fury: Velen. If you did that quest or remember it, this one works mostly the same exact way. You'll go to multiple locations (all of which shown on your map and the map above) and fight someone there using only your fists.
At each location you'll be able to bet on the fight - so just place the maximum bet on yourself and win each time. Georgius will ask you to throw the fight against him, much like Fishgulper did for the Velen quest. If you do throw the fight against him you'll have to fight him twice for quest credit.
Defeating all three people will unlock the final fight against Durden, Tailor Durden - a reference to Fight Club. When he arrives on the scene you'll also get a reference to Knight's Tale as well, as shown in the screen shot below.
Beating Durden will complete this quest.