The world's first underground railway was built in:

An underground railway (also called a metro, subway, or tube) is a rapid-transit rail system that runs mostly through tunnels beneath a city, built to carry large numbers of passengers quickly without adding to surface road traffic. The world's very first such system was a 19th-century steam-hauled line built using cut-and-cover tunnelling.

The Metropolitan Railway opened to the public on 10 January 1863, running underground steam trains between Paddington and Farringdon Street. This made it the first passenger-carrying underground railway anywhere in the world, and it later grew into today's London Underground.

• New York's subway (built by the Interborough Rapid Transit Company) began passenger service on 27 October 1904.

• The Delhi Metro's construction began in 1998, with its first line opening to passengers in December 2002.

• The Dubai Metro is a fully automated system that began operations in September 2009.

The Metropolitan Railway therefore predates every other listed city's system by decades, confirming this location as the correct answer.