Concerns wiring Ethernet in House
I would put it in the closet and put an outlet in there as well.  8 wires coming out of the wall is quite messy and having this in your office behind your desk is quite unsightly and hard to organize.

I'd suggest drilling down through the top plate and running both power and the network drops down into the closet wall.  I would use separate holes for the cat6 and power to keep them apart.  Mount a 1/4 inch sheet of plywood on the wall to the studs, this gives you the freedom to mount the network switch wherever you want and gives you a better handle on cable management.  Sand and paint it if you want it to look good.

WRT the coax.  You can either keep the cable modem at the desk and run an ethernet port to the office desk or, as you suggested, put it in the closet.  I would opt for the closet, but instead of running the coax under the door, I'd run that in the wall as well.  You seem to have good access in the attic, so you have the freedom to run an extra cable.  I'd go up from the box where the existing cable is, connecting them with a barrel, and run the new cable into the closet.  

No cables on the floor, no bundle of wires coming out into the office.  

Remember to seal the holes you drill into the top plate with fire rated caulk after running the wires through them.