First, I would try living with that TV up there for a month before doing anything. The TV is way too high for comfortable viewing, especially given that couch placement. It will likely cause neck and eye strain.
The columns on either side of the fireplace are most likely hollow and would provide the best option for running wires. You could either place a box on either side and pass an HDMI cable through, or simply run it down into the basement. I would use an HDMI switch near the components so that you only run a single cable up to the TV. It will be cleaner and easier to hide. You can purchase HDMI cables in various colors from monoprice.com, so you can match your walls. If the TV spans the entire width of the alcove, it should end up giving a clean look.