When Jimmy Fallon took over the "Tonight Show," he brought the entire thing from the West Coast to the East Coast. In 2015, when Stephen Colbert succeeds David Letterman, the show will remain in New York City, and the "late night" war will have at least two shows right down the street from each other.

According to the Hollywood Reporter, even though there were rumors of a West Coast move, the "Late Show" is here to stay in NYC. CEO Les Moonves had this comment,

We’re thrilled to continue broadcasting CBS’s Late Show from New York and call the Ed Sullivan Theater its home. David Letterman has graced this hall and city with comedy and entertainment that defined a generation. When Dave decides to pass the baton next year, we look forward to welcoming Stephen Colbert, one of the most innovative and respected forces on TV, to this storied television theater for many years to come.

There still has been no final dates for David Letterman's run in 2015.