Couple problems I see. First is the textured ceiling. You'll never be able to open that up and patch it without being obvious, the texture is something that just isn't done these days. Second, the exterior wall should have insulation in it, so you'll end up fishing the line through insulation and the vapor barrier.
Instead, I'd suggest running the line around the floor if you can get it to a convenient wall anywhere in that room. Use some fasteners to keep the cable at the base of the wall to run it around the room:
National Electrical Code 2014
Chapter 8 Communications Systems
Article 800 Communications Circuits
I. General
800.24 Mechanical Execution of Work. Communications circuits and equipment shall be installed in a neat and workmanlike manner. Cables installed exposed on the surface of ceilings and sidewalls shall be supported by the building structure in such a manner that the cable will not be damaged by normal building use. Such cables shall be secured by hardware, including straps, staples, cable ties, hangers, or similar fittings designed and installed so as not to damage the cable. The installation shall also conform to 300.4(D) and 300.11.
Chapter 3 Wiring Methods and Materials
Article 300 Wiring Methods
I. General Requirements
300.4 Protection Against Physical Damage.
(D) Cables and Raceways Parallel to Framing Members and Furring Strips. In both exposed and concealed locations, where a cable- or raceway-type wiring method is installed parallel to framing members, such as joists, rafters, or studs, or is installed parallel to furring strips, the cable or raceway shall be installed and supported so that the nearest outside surface of the cable or raceway is not less than 32 mm (11⁄4 in.) from the nearest edge of the framing member or furring strips where nails or screws are likely to penetrate. Where this distance cannot be maintained, the cable or raceway shall be protected from penetration by nails or screws by a steel plate, sleeve, or equivalent at least 1.6 mm (1⁄16 in.) thick.
300.11 Securing and Supporting.
Please see NEC for full text
So basically, you're going to want to protect and support the cables in a similar manner to any other cables. Curiously, the code didn't mention 300.4(A) Cables and Raceways Through Wood Members.. Though I'd likely still follow that section if I had to run communication cables through wood members.
If you run the cable through conduit, you'll have to follow the code for protection and support (fill requirements do not need to be met, per 800.110(B).
If you run through a drop ceiling, you'll have to install support wires for the cable, or support it in another approved manner. You can't support the cable using the ceiling grid, or support wires.
Here's a great document from Mike Holt that explains Article 800 (with images).
Introduction to Article 800 - Communication Circuits (PDF)
Best Answer
To help you with the terms, what you're looking at from above is the top plate. Frequently there are two 2x4's for a top plate. Two boards are used for added structure at the joints and extra fire proofing. This gives you about 3" of wood to drill through.
As ChrisF mentions, you should run a stud finder up and down the wall cavity near the halfway point to see if any fire blocking has been installed. This would be a single 2x4, and will almost always be in a wall if the ceilings are over 8' tall.
You'll significantly reduce the odds of insulation in the wall if you are doing this project on interior walls. You should also be avoiding any electrical in the same wall cavity (between the same two studs). You would see an outlet, switch, or wire coming out of the top plate if this were the case.
As for the actual wiring, I've used these low voltage mounting brackets for the hole in the wall. Place the bracket on the wall where you want the opening, mark the corners and sides, and cut out the drywall with a drywall saw. Test fit the bracket and file back any spots that are blocking you until you get a snug fit. Then bend the tabs back into the wall and tighten them with a pair of pliers. On that bracket, I use a modular plate (these comes with more openings if you need them) and then an ethernet jack mounted in the plate. You can also get jacks for cable, phone, stereo, etc.