We visited Norfolk for the first time a few years ago thought it was very nice, particularly remember Wells by the Sea, Holkham Beach, Holt and Burnham Market awash with posh Londoners when we were there, I thought they were all down in Cornwall, but obviously not! Did a tour of Sandringham, particularly remember the stately motor cars from a bygone era. We stayed in Hunstanton, didn't seem too hoity toity or down at heel either.
Also visited Northumberland more recently, yes once again lovely, stayed in Alnwick, great town fab castle and that wonderful Barter Books, what a place that is! I could have spent all day there and it had a lovely cafe and lots of nooks and crannies to sit and eat their cakes and scones. Also loved Seahouses nearby and remember a spectacular beach over looked by Bamburgh Castle, I think? To top it all Lindisfarne, well worth a visit.
Never let it be said of me that I slag off anyone else's county