If that doesn't work, and you either don't look up often or you don't mind a little ugliness, I've found running cable along the tops of walls near the ceiling works pretty well, and is easy to do. Here's part of my home network cable run and also part of the speaker cable run for the right rear surround sound channel [1].
Where a cable needs to make a turn to follow a corner, I screw in a cup hook. For support along a straight section of wall I nail a wire nail partly in and hang the cable on the protruding part.
If you want to do the work, adding in crown molding after running some cat6 can make the room look much nicer if the style fits. You can then drill a hole in the drywall at the top of the wall, drop the cable down between the studs and install an actual outlet. Crown molding usually has a decent amount of space to run a few cables.
As others have said, crown molding can help that. Also, there are flat cables that can make running cable between baseboard and carpet (and even under carpet) virtually invisible.
Staples leave small holes when removed which are easy to patch. You can also use many of them to get nice straight and tight runs. You can put a bit of white (or whatever color your walls are) paint on them to help blend in.
It's not ideal aesthetically, but nice straight lines and right angles go a long way to making it look better. The next step up would be to run some channel to hide the wires, but I don't find that necessary.
Careful with the staple gun. Some of them are more powerful than you might think, and are potentially capable of pushing the staple through the insulation and providing a nice conductor to connect the wires. It has happened to me.
Where a cable needs to make a turn to follow a corner, I screw in a cup hook. For support along a straight section of wall I nail a wire nail partly in and hang the cable on the protruding part.
[1] https://imgur.com/GVEiubN