So how do you hang a TV on the wall, centered above your fireplace, with no stud in the center? Here is a little tutorial from Dave on how we did it:
You'll notice in the picture below that, not only was there no stud anywhere close to the center of the fireplace, there was a block of concrete where the old stove flue connected to the chimney.
A cross-section would be worth a thousand words:
Essentially, mount a "structural" piece of 3/4" plywood solidly to your studs (3" countersunk screws were our choice). That will allow you to place your TV bracket anywhere between those studs and still have a considerable amount of meat to bite into. Use caution and common sense when doing this because you'll probably not be able to use the bracket manufacturer's provided hardware. You may have to buy some short and stout lag bolts and washers from your local home improvement store to get an adequate bite over 1" or less of material. Our TV was only a 32", so it was pretty light. Still, the bracket was attached with four lag bolts just to be sure.
Next, just hide your "ugly" structural piece of plywood with something decorative. We chose beadboard and framing. This was a purely practical solution to a problem, but that doesn't mean you can't make it look good!
Finally, if you're an unfortunate soul that has your drywall torn out near any media center, do yourself a favor and purchase some large conduit pipe and bury it in the wall. What you don't see here is almost as important as what you do see. What you don't see are the power cord, two HDMI cables, and the potential to run a VGA cable to our TV. With the conduit I was able to neatly run the cables to the TV now but I still have the ability to switch out the cables to the next best thing in 5 years. The conduit went from an opening behind the TV to the attic. Then we had another piece of conduit running down the wall behind the side table to the right of the couch. It ended with an outlet on the wall where we could connect the DVD player to the cords we routed from the tv through the attic and down that wall. I hope that makes sense.
Ultimately, something we weren't able to do was connect our old desktop computer to the TV. We were planning on buying a wireless keyboard and mouse, stashing the desktop in our hallway nook, and running a 25' VGA cable to the TV to use it as a monitor. Great for picture slide shows at parties or streaming Hulu/YouTube/Netflix.