Brasilian Japanese fusion food definitely exists in Liberdade.

Does Sao Paulo have food exclusive to the city ? I imagine so. Do I know much about it, not really. The mortadella sandwich seems to be the only thing that comes to mind. You can google for that and you'll find places everywhere close to your location. It's pretty good IMHO with an ice cold beer.

Now food preferences, all depend on the individual, and as a gringo who has moved here permanently, my experience as a diner tends to lead me to believe that the best grub is to be had in the more local and downscale of places. So, look for older street botequims or boteco's, pe sujo bars, etc, as they are likely to have a middle aged or later female chef in the back making food like her mother, and grandmother did. The corner bar where I live has seats for about 30 and a woman who creates these awesome dishes on a daily basis. For R$60, about $12 USD (their most expensive thing on the menu BTW) I get a homemade churrascu meal with 4 kinds of meat, fries, rice, farofa, and molho a campanha. It comes on two plates and is heaven for my stomach. I can go to an upscale fancy place and pay 3X or more as much for food that tastes the same or worse, but it'll have a waiter dressed like a penguin instead. Your call obviously. Lot's of fancy high end restaurants back where you live I imagine too. If you want a real experience try one of these places. They will all have similar signage, chairs out front, etc, and usually a sandwich board with the day's menu on it. No one will speak english, but always smile, use google translate, and they'll treat you like one of their own.