Switching PC between two TVs
I recently built a nice little home theatre PC, which is sitting in the loungeroom and hooked up to our big TV, but I'd also like to be able to hook it up to the TV in our bedroom, so I can play games without tying up the big TV. I've already ran a long HDMI cable from the lounge to the bedroom TV, and I have a wireless controller, but right now the only way I can switch the PC between TVs is to unplug one HDMI cable from the back of the PC and plug in the other, which isn't a good long-term solution.
Has anyone set up something like this? I figure there are a few ways I could do it:
* Get a HDMI switch -- there are some cheap two-way switches on Amazon. Is there anything I need to worry about with these?
* Get a HDMI splitter -- this sounds like a great idea, since I won't have to do any switching, but given that HDMI is a negotiated protocol, I don't like the look of some of the cheap splitter cables I've seen
* Connect both TVs to my PC -- my video card (an EVGA 750Ti) has a DisplayPort output in addition to the HDMI output I'm using, so with an appropriate adapter I figure I could connect to both TVs and just mirror the display on the card. Will a passive DisplayPort adapter work for this, or do I need an active adapter? How would sound work -- would the card output the same sounds to both ports?
* Is there some other, better way to do this?