Consider Boxee Box, Dune, or PopCorn Hour media players, among many now on the market. They connect to your home network (wired or wireless), and output VIA HDMI (or component and digital audio...) to the "dumb" TV's. You can then either play local media from networked computers/dedicated HTPC or better a NAS server, or stream from many internet sites such as Netflix, Pandora, Hulu etc.
No special additional software is needed. The source of local media just has to be set up as a share (e.g. allow one or more folders to be shared across the network) so it can be discovered by the media player.
Live TV is a bit more gnarly. You could have one or more tuner cards in the HTPC act as a server and either record for later playback, or relay a live stream...I have not done that myself but perhaps others here will chime in. IMHO I'd just put a CATV settop box (or distribution from an antenna if you would rather go OTA) at each location needing live TV.
The form factor of the Boxee is the smallest, but may not be the easiest to hide; it looks like and is about the size of a Rubik's Cube, with one corner cut off. Most other players/extenders look like traditional A/V components, one or two rack units high, and no more than 19" wide. They fit in well with other A/V equipment on furniture shelves or equipment racks.
Hope that gives you some ideas...
Mike