Daily City is a news service in The City. It is very likely that Daily City is heavily monitored and censored by the City. Though there is information suggesting the opposite is true: in an elevator in the Robert Pope & Associates Building there is a news feed, showing an editorial written by Robert Pope. Seeing this is the competitor of the current mayor, Callaghan, it isn't very likely to see this on a news feed, it would probably have been censored. But it hasn't, so that might tell us something about this company.
City Eye would be the logical competitor of Daily City, though City Eye seems to be more important, as it has helicopters and has ties with the City (it provides information to them, for example in the chapter "The Edge" of Mirror's Edge, when they alert the City Protection Force of a Faith Connors on the rooftops). Daily City advertisements can be found all around the City, with the slogan "All the news you need!"