
Have you tried the Holiday Inn Express ones? There is a one on the A19 at the Sedgefield junction which would be about 30 mins from Newcastle (depending on exactly where your show is) and then about 50 mins to Newby Hall. Closer to Darlington, but still only about an hour from Newcastle, there is a little "village" hotel called The Angel, at Topcliffe - it is only a few mins. from Newby Hall, dog friendly and fairly reasonable, usually.