Currently I'm running an HDMI cable from my Sony BD player to my Sony TV. Then run a digital cable to my Yahama receiver from the TV. Would I get better sound quality if I ran HDMI to the receiver and then HDMI to the TV?
Probably; and BD to receiver, receiver to TV i sthe recommended connection path. Most TVs only send stereo through the optical out (except for their tuner signal, which goes out normally). Also, If your receiver can decode HD audio, then you are also missing out on that.