The Dragon's Den studio at the BBC's Salford site is in Salford.
Salford is a city in Greater Manchester and the location of MediaCityUK, a major centre for television, radio and digital media. The BBC moved significant operations to the Salford site, where studios and production facilities support a range of programmes, including Dragon's Den.
The location is often described broadly as Manchester because Salford forms part of the Greater Manchester urban area and lies directly beside Manchester. However, the specific city named for the BBC's MediaCityUK site is Salford. That distinction matters when a question asks for the city rather than the wider metropolitan region.
Dragon's Den has also been associated with other production locations and studio arrangements during its long broadcast history. The answer here refers to the BBC's Salford base at MediaCityUK, not to the broader region or to a previous filming location.