...to two of your three requirements is to head north from Dallas to OKC on I-35 and pick up the parts of old US-66 just west of there. I don't know that that would satisfy your request for the 'nicest' route, but any other routing is going to seriously violate your desire for the 'shortest' route.
You do realize that US-66 has been decomissioned and thus technically doesn't exist anymore, so what you'll have to settle for are segments of what used to be the Mother Road, but now more typically carry state highway numbers. The section just west of OKC, for example, is OK-66.
Hope this helps. If there's something more specific about 66 that you're trying to capture, just speak up.
AZBuck