Just as a heads up, Cox phone service is not available throughout the city. When we were on the East Side, we had all of our services (phone, internet, cable TV) bundled. Not only was it cheaper, but it was so much more convenient to only keep track of one bill.
Unfortunately, when we moved to the West Side, the Cox phone service was not wired for our block. As such, we had to go to Verizon for phone - ugh. No joke, on the very day I called to set up the service, I was already receiving rude customer service (the Verizon person argued with me and told me that Working Assets was not a long distance carrier). Needless to say, we miss the days of Cox telephone.
I'm fairly certain that Cox offers HD service (our digital cable has HD channels which we cannot receive - no HD TV), but don't know about the terrestrial signals.