Yes, you can run a TV tuner on one monitor and have your computer on the other. I have one built into my card, and I have dual monitors.
That my be something that you would want to spend some money on so you can get one that dosent suck. In the case, you get what you pay for. Just think of it as a video card. eVga is a really good company, and they have a few on there. A little expensive though. Or check the ASUS. Anything ASUS makes will be good.