If you are running 1 HDMI, then run 2 and if you are running 1 cat-6, then run 2. This is ten times as important since you do intend to do some sound isolation work.
All cabling should be brought to a blue box which is depth adjustable and then sealed on all entry ports with firestopping to help prevent sound bleed. Just like an outlet plate requires the same, you can do this with HDMI and Cat-6 cabling just fine, and it should be approached with the same mentality.
Similarly, running conduit within a sound isolated space, should be brought into a blue-box, cut a hole in the box the proper size, then seal the edges so sound doesn't pass around the edges.
Depth adjustable electrical boxes: