Can I drill through joists?
The method you describe is the basic method used by electricians and data-techs to install low voltage cable.

Low voltage and data cable do not require conduit where it is exposed, or full boxes in the wall. It does need to be run through the floor joists in the basement and stapled to the tops of the ceiling joists in the attic.

Normally you would install it similar to how you have envisioned. If there is a basement, you would drill up from the basement into the wall cavity and cut a hole in the wall sized for a device box. Cut the hole at the same height as your receptacle boxes so they all look even. Make sure you don't hit a stud. Most data-techs use a long ¼" feeler bit with a slot in he end of it. Once you drill up where you can reach the drill bit you attach the wire to the drill bit by twisting some of the wires through the slot in the bit. Then pull the wire down into the basement and feed it to where you want to go. In the basement the cable needs to be run through the floor joists.

If there is no basement, or you think it would be easier in the attic, then drill down into the wall cavity as you already attempted. Make sure your drill bit is long enough to go through both of the top plates of the wall. (This can be a problem if you are near the perimeter of the house where the roof slopes close to the top of the wall) Then use a fish tape in the wall to reach the hole for the data-port. Pull your wire up from the main floor and feed it through the attic to where you want to go. Sometimes you can use a short length (10 feet) of small chain or solid wire fed through the hole into the wall cavity and use it to pull the wire down from the attic. (This is all much easier with two people.)

Either way you go you should read more about the design of wall construction similar to this article. Take accurate measurements to locate the wall cavity and make sure you don't drill into open floor or ceiling.

Good luck!