Cox does not charge extra for HD channels but you do pay for rental of a HD set top box which may or may not be a DVR depending on what you want. FWIW here are my current charges per month for Cox cable service including a SA 8300HDC set top DVR box.
Quote:
Cox Limited Basic 1 11.75
Cox Expanded Service 1 37.75
Digital Service/Digital Gateway 1 6.00
Movie Tier 1 4.50
Sports & Info Tier 1 2.25
Variety Tier 1 2.25
Discovery Tier 1 0.00
HD Expanded Tier 1 0.00
Cox Digital Video Recorder Service 1 11.99
Digital Converter - DVR/HD 1 5.25
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If your HDTV has an internal QAM tuner, which I believe all new TVs have, you could get the local channels, ie. ABC/CBS/Fox/NBC for example, in HD without the set top box or associated charges by simply plugging in the cable to the TV and doing a digital scan. You will not get channels like ESPN, Encore, Discovery, etc for example without the set top box.
If I remember correctly Cox supplied component cables when I initially got my old SA 8300HD set top box. If you want to use a HDMI cable you need to purchase that yourself. At least that is the way it worked here in the OKC market. Don't buy expensive Monster cables. Walmart or Sam's Club have good deals on HDMI cables as do other sources online.