Almost every modern graphics card has an HDMI output.
Any basic graphics card like an HD6450 would be fine to add another monitor (or HDTV I assume) however you wouldn't want to play games with it.
If you have a regular monitor AND an HDTV you would have to setup your TV separately in the video control panel. You would also have to switch the AUDIO output to use the HDMI version if switching from normal output to HDMI output.
HDTV setup:
In the video control panel, it's setup a little differently. More like:
HDTV section-> 1080p_NTSC@60Hz, then
adjust overscan