I'd prefer Route 1, as I cycle some of those roads most weekends (near Bellingham and Rothbury particularly, and out into the Cheviots, occasionally up to Wooler)
Suggested route 1
Angel of the North - Blanchland - Corbridge - Hexham - Allen Valley - Cheviots - Bellingham - Wooler -Rothbury - Newcastle - Tyne Bridge - Gateshead Civic Centre
Suggested route 2
Angel of the North - Slaley - Crawleyside - Edmondbuyers - Stanhope - Wolsingham -Hill End - Bollihope Common - Richmond - back up to Allendale via Cowshill (finish in Northumberland.)
And not forgetting Gateshead’s very own climbs and cycle routes with a view....
Bensham Bank, Chowdene Bank, Long Bank, Rowlands Gill to Blaydon, Springwell to the Team Valley.