Info from Wikipedia
Late Show with David Letterman is an American late-night talk show hosted by David Letterman on CBS, the first iteration of the Late Show franchise. The show debuted on August 30, 1993.
In 2014, Letterman announced his retirement; the final episode of Late Show aired on May 20, 2015.
The show was taped at the Ed Sullivan Theater at the corner of Broadway and 53rd Street in midtown Manhattan during its entire run.