It's only the US, but as a start, the Bureau of Economic Analysis (BEA).
Gross Domestic Product by Metropolitan Area
Real gross domestic product (GDP) increased in 292 metropolitan areas in 2015, led by growth in professional and business services; wholesale and retail trade; and finance, insurance, real estate, rental and leasing, according to statistics on the geographic breakout of GDP released today by the Bureau of Economic Analysis. Collectively, real GDP for U. S. metropolitan areas increased 2.5 percent in 2015 after increasing 2.3 percent in 2014.
There is historical data, until 2015 at the time of writing, which can be corrected for inflation.
Each region can be divided into industrial sectors.
There is a data explorer tool and a programming API