[jblz]

I'm pretty sure Cable boxes all have HDMI these days, so that shouldn't be an issue.

Monitors won't have an over-the-air tuner, so, you'd need to use an external device to watch broadcast TV.

[rufus_foreman]

You don't need a cable box or a TV to watch cable TV anymore, you can stream it over it the internet.

HMDI from a computer to a monitor or a projector would work fine.