Moving a router

What kind of router do you have? If is has a cable connection on the back, then it's actually a gateway, and should work anywhere there is proper cable signal. TV signal and internet signal can coexist on the same wire.

Alot of it will depend how that outlet is wired. I would suggest moving it and then checking the signal levels at that location. You can either call up and ask Cox to look at your signal, or you can see it via the devices diagnostic. I can give more info on that once I know what modem/gateway you have.

Another thing to consider is where you're moving the gateway inside your house. If the new room is in the basement, or in the corner, you might lose wireless signal strength to other parts of the house. Just FYI