I also have Century Link but we have no modem. Whenever I call them they refer to my service as 'to the curb'. We do have a Century Link box in the garage but it's a plastic wall box that's labeled 'Cyper Power'. I was told there was a backup battery in the box, so in case of a power failure we wouldn't lose our phone or internet. Last summer our phone/internet went out for the only time in 4-1/2 years and when the tech came, he said apparently a nearby lightning strike had knocked out the battery and he put a new battery in the box and service came back.
Anyway, I can show you where we put the router in our courtyard villa. Century Link put one double jack inside our house, it's at the end of the bar on the partition wall at the far right of this photo. One jack is for telephone and the other is for internet. We just plug our router directly into the wall jack. The bar is two-tier, so the router hides below the top of the bar and just inside the wall. Our smart TV is about 25' away and our laptop we can take anywhere.