The schools in Newcastle such as Central High / RGS are far better than Sunderland High. It's an ok school in terms of facilities and teaching but bizarrely my best friends children have developed awful accents whilst there. There aren't many good schools to choose from in Sunderland having said that. St.Anthonys/Aidans/Roberts are the best.
Emmanuel college is halfway between Newcastle and Sunderland I believe (although I could be wrong, am not native and my geography is appalling) and has a fabulous reputation. It is a CofE school but the ethos doesn't seem too religious IYSWIM?
Have you considered Dame Allans in Newcastle? Im(h)o its a fabulous school which represents the best of both worlds. Single sex education yrs7-11 (but both boys and girls schools on the same site), coeducational sixth form. It maintains that small school friendly/family feeling, yet has a large school outlook and gets good academic results. My experience is that I used to work there so possibly slightly biased , but is definitely worth a look.
I don't think RGS is that hard to get into. I used to teach in Northumberland and several of our children got into RGS just by taking a set of tests in school. They were bright kids but not outstanding.
Barnard Castle too far? Pollam Hall in Darlington?