I know it may not be the first thing electricians think about but maybe you should ask your wife where you can put a box.
It is always a compromise between aesthetics and the reality of where you can get the wires to go.
I would go with a bell box on the outside wall, then you have a lot of flexibility. I am also a 3/4" smurf tube fan for things like this, not the "LV" orange stuff.
I put a lot of smurf in my last remodel and after it was all done, I still need another one. My wife put a TV where "there will never be one". I am left with a cable strung 8' across the floor from the nearest LV box.
My house has 2x4 framing. I think Raco makes 4-square boxes of a 'double depth,' that would have a 'front' face even with both sides of the wall. Just put mud rings on both sides, face plates as usual.
You know, that might be just perfect for this task.