The upstairs room solution is pretty obvious go vertically up through the wall in the computer room into the attic space run the cables to where they need to go then drop then down into the rooms punch them into the back of a wall plate done.
Cable drop through attic multistories.
I have run the odd cable in my house wood frame wallboard by drilling down from the attic into the hollow wall.
Drill holes in the floors as per your markings by using a power drill equipped with a 5 8 inch drill bit.
There s a 2x4 at the top of the wall with vertical 2x4 studs.
Step 4 drop the coaxial cable through the holes in the floor until it reaches the connection in the basement.
To drill through a rug make a small cut in the rug with a utility knife and then drill down through the cut.
Use a piece of string that you can add a small weight to such as a steel nut or whatever you can find.
By using a drill bit sized large enough for the cable.
For single floor homes with a basement the basement may be the best path.
These methods will work for any cable telephone network thermostat power etc.
I ve mounted a junction box on the stud by cutting into the wall then made a small pilot hole into the attic through the ceiling to register the main hole through the 2x4.