How can I run a coaxial cable into an existing single gang electrical outlet?
Have you thought about trying to achieve the same result without running wires?  Assuming you're using a cable (or satellite) box of some kind (and your TV doesn't have a built-in cable card), you could use something like this:



That would give you a standard RCA connection from your satellite/cable box to your TV.  There are other options for other connection types; e.g. this one for HDMI (although it gets spendy). 

Failing that, how about just using a quarter-round cable cover around the edge of the room?