You can stick with "Basic" cable - but get 5-10 HD channels even from Time Warner.
I got a HD-DVR, "Basic cable" which included 7 local stations for $24/month.
Dont let them up-sell you - just tell them you want basic service, but include the local HD channels.
The cool part about TimeWarner - no contracts. Many of the others require a 2 year commitment.
Also - type your address into
www.antennaweb.org and see what over-the-air antenna stations are around your home. You may be able to get away with a indoor antenna so a $24 investment in a "Phillips Silver Sensor - Classic" antenna may give you free HD channels.
http://www.repaircable.com