Metro City (Riverton, Ohio in the live action films) is a city with buildings resembling those from Pittsburgh or New York. At one point, it was declared "America's Safest City" when Dr. Claw and all the criminals were behind bars. Its notable residents are Inspector Gadget, Penny, Brain, and Chief Quimby.
Apparently, Metro City is infamous for Dr. Claw and his M.A.D. Agents constantly trying to take over it, with Gadget always foiling his plans. The city is either located in the USA or Canada. But in the 2015 series the city is actually located in Canada but this is likely because DHX media (now wildbrain) is a CANADIAN animation studio and entertainment company as they were the ones who animated the 2015 series.