Even in an internet age, there must be something that television provides that the internet doesn't. The most immediate thing I can think of is that television is localised by default. As the internet swallows up popular entertainment and world news, it's possible that television will move to exclusively local content. You'd get ads and public access shows from your city (or even just your suburb) and very local news. There'd be no need to cover global events, because people will be getting that news from the internet.
In the end, it might even help revitalise a sense of community, although I wouldn't count on that. If television becomes such a niche market, television sets will become less common as a result.
Mokalus of Borg
PS - Though we may still have large screens for sharing entertainment.
PPS - Or family-to-family video calls.