Walls and Ceilings - Drilling Question

So I'm going to hang my new 52" Sammy A750 LCD on the wall above my gas fireplace (I have never used this fireplace so it will never be on -- it is just the best location in the room for the TV).

Anyway, using a stud finder I've determined that on either side of the fireplace is a "large" stud. By large I mean wider than the standard 2x4. I'm not sure if this is two 2x4's right next to eachother, or what, but I assume it is a load bearing stud. (Please, correct me if I'm wrong).

I need to run a single romex cable through the thick stud from a socket that is to the right of the fireplace so I can pull it up above to have the TV plug into.

I also will need to drill through the left thick stud so I can run the HDMI and component cables down to the corner of the room (I will also have to go through a ton of 2x4's which I am not looking forward to) to the AV equipment.

Can anyone let me know if I'm making any glaring miscalculations here, and if not, how big of a hole can I drill through the load bearing studs without violating code? Also, where would be the best locations to cut the drywall out so I can try to get a drill in there to drill through the stud (which would make it easiest for me to patch/mud in the end?)

Any help would be appreciated. :-)

A 5/8" or 3/4" in hole in the center of the studs would be fine. The easiest hole to patch would be cut in the middle of two or more studs so you have structure to screw the piece into when you put it back in.

Poke through the drywall with a very skinny icepick to verify your readings.
Using pressure and twisting, try to determine if you're hitting wood or a heating duct or a pipe or concrete or a nailing plate covering Romex.

If the readings are wrong, you can spackle the holes.

I like WDIBAA's suggestion for investigation first. I'd start that way.