Well, alternatively you can run a second video output from the one box you rent to the second tv, but you will be limited to the programming being viewed on the one box.
I'm not aware of any PC based cable card solutions, currently, but some may exist or are being developed.
The trick is you need a way to let TWC know you're authorized to view their encrypted (digital cable) content. You need either a cable box or a device that can take a cable card. Without a cable card and just simply a QAM capable ATSC tuner, you can get some channels that are unencrypted, but those are generally local channels and some that may pop up and disappear.