Before I had a child, I stuck to using WiFi to get access in the room with my PC in- not ideal, but worked, not a huge problem. However the router was simply rubbish and before long the signal was getting interference from the microwave, short wave radios, M15 and low flying flying saucers- Cat5 had to be deployed.
Unfortunately my landlords were against the idea of an in-wall solution, so I had to "externally" do it. I ran it from behind the TV cabinet where the router was, over a doorway and along a skirting board, behind a sofa, under and up a set of stairs, up to the ceiling and over another doorway before finally slipping it under the doorway (as there was clearance with no catching) and along the skirting board up to my rack upstairs.
The whole thing was accomplished in the course of ~2 hours, using nothing more than cable clips and some gumption. If you didn't already know it was there, you'd not notice it. I left some slack both up and downstairs before terminating the ends, just in case.
There's ~12inches of space behind the TV unit and the wall where the cable starts- though it's in a corner so you can't really get behind it if you wanted to. The only spots he could realistically "get" at would be the doorway next to it, as the run goes up one side and down it.
He hasn't, in all his years, even thought about it until a few months ago when he was into his 7th year- even then it was just to ask what it was!
I'd say that if it's just in the wall, in an area that you can cover with furniture of some variety (or even something lightweight that will just cover it- like a laundry basket or material shoe rack) that should be enough. If you can hide it behind something more sturdy, all the better.
The only other solutions you'll have are the before-mentioned covers that work with power cables, or a very robust outside enclosure that's designed to be weatherproof- as these can often be secured with a padlock (or cable tie). If possible, the only cheap idea may be to cover it with a wiring junction box cover which could be screwed into the wall over the top of it, but the cable will still protrude and potentially get yanked on.