Yes... hard not to sound negative on this one..
Japanese people love foreign food..
Italian, French, Korean.. even Chinese...
But American food is not exactly famous as international cuisine or for being healthy..
McDOnalds and Dennys do OK here.. but they adjust their menus for Japanese tastes..
Also.. for this you would need a business visa.. not a work visa..
so you would need YEARS of experience owning a similar business and LOTS of cash to prove you can do it.. and employ at least two Japanese staff - those are the rules..
Sorry the news is not good..