Hi there,
The Caravan Club have a nice site within a 10 min drive of A1 at Scotch Corner.
The Site is Hargill House, it is listed as Richmond in the CC books but backs onto the A66 very near to the interchange and services with the A1 at Scotch Corner.
I have not stayed at this site, however I did visit it whilst passing one day. I thought it to be a very nice quiet site with nice views facing south over the fields and Hills, I would also recommend pitching to the south side of the site as the North side which sits adjacent to the A66 main road may suffer from some traffic noise.
A little further up the A1 you have the The Grange CC site at Durham, this site is situated just off the A1 therefore ideal as a stop over, there is also a Tesco etc quite nearby as well as Durham City centre.
Hope this helps!
Cheers!
Andrew