This is unlocked with Kazama's Real Estate Royale minigame. Although you may unlock this by completing any of zones in the district, the easiest (least amount of yen) will be within the Leisure King area.
There are two side quests to complete to fully own all properties within this area: Befriending the clerk at Poppo Tenkaichi St. and the amateur sushi chef at Sushi Gin.
Befriending Miho is simple by buying items at the store and correctly answering two questions. 1) suggesting the store to accept Parcel Delivery Service and correctly guess the new menu item Miso Cutlets.
Befriending the chef at Sushi: you will have to first eat sushi for a couple of visits and then later supply fresh fish to the store. You will have to either fish by taking a taxi to the pier or by either buying fish from the black market or randomly from Dream Machines.
The two quest properties are given to you for free after befriending the two characters.
After owning all the properties in the area, slowly upgrade your buildings to S rankings until you reach 100% share.