Not sure if the old sudios are still standing, but they have offices on the Kingstown Industrial Estate to the north of the city with a newsroom and (aiui) an advertising sales team. They occasionally broadcast from the newsroom if they need to throw to the newsroom for an update on a breaking story on Lookaround.
Border TV's Studios are now demolished. There is a new Bureau/newsroom in the Kingstown area of Carlisle for the 3/4 main correspondents and newsroom journalists. 6 Location Journalists (spanning Edinburgh to Cumbria) work mostly from home.