The old Daily Mirror pub was officially the White Hart, but everyone called it The Stab, as in the stab in the back and there's also the Cartoonist round behind the old Express building in Fleet Street.
I can't think of any with names that are particularly newspaperish however, though there are plenty of pubs around Fleet Street with long and inglorious associations, including The King and Keys (Telegraph), The Punch (Standard), The Harrow (Mail) and the Tipperary (News of the World).