I'm guessing your Internet cabling is all Cat5 (or Cat6 or whatever Cat) cable. Unfortunately, you need coax cable instead for signal distribution, unless you use a "trick."
I'll describe the "trick" first in case it appeals to you. It's simple: buy an HDHomeRun (or two or three; you can start with one and add more later as needed) and hook it/them to your in-home network. Then split your antenna signal and feed the HDHomeRuns.
The problem with this trick is that you need either DLNA-compatible TVs, PCs, or PC "extenders" to stream video from the HDHomeRun(s) to your TVs over your network. (If you use Windows Media Center on your PC, you can use cheap XBox 360's as extenders for it.)
But if that's not for you, you'll need to run coax cable from an antenna to a splitter and from the splitter to each TV. It will be a completely separate cabling system from your network cabling, but you can run the cable through the same drops in your home and put in dual coax/Cat5 face-plates if your TVs are where your Cat5 cable outlets are.
TWC won't help you set up an OTA system, but you might be able to convince TWC employees or ex-employees to help you on their own time. Or you could "cheat:" subscribe to TWC just to get them to install cable, then after a month or two, cancel cable, disconnect their cable feed (they might do this themselves, but just in case) and connect it to an antenna instead.
One more thing: if you have more than, say, two TVs, you may need to put an amplifier between your antenna and the splitter to keep the signals from getting too weak. I usually recommend the Winegard Boost! amp if you need one.