OK. This is what I would do. Bear in mind I don't know the area at all but I just enjoy planning routes! This route is from a combination of Google Earth and the Sustrans routeplanner at
http://www.sustrans.org.uk/
It's a 12 and a half mile ride in total, and adheres' to my personal natural habit to avoid all busy roads at all costs !
I'd head up the B1296 for two miles. Then left along Shipcote Terrace, right into Avenue Road then left down Wesfield Terrace, Dunsmore Grove and Armstrong Street (under railway line). Right up Ascot Crescent then left along Lobley Hill Road. After 100yds or so join the cycle path north. Pass under A184.
Then join the Tyne and Wear trail along the A114 heading west. It's down on the Sustrans site as off road cycle track but it looks (from Google Earth like one of them crap shared pavement jobs). Anyway at Cross Lane go under railway bridge then immediately right onto a proper bit of off road cycle path. Follow this to the bridge over the Tyne at Scotswood and cross it.
Then join Hadrians Wall path (cycle path too) on other side of A695. Follow that north for a couple of miles past the big A1 roundabout. Then cross A1 over ped bridge. Go west along Burwell Avenue and right into Thornley Road. Go along path at end of road some way & pass under Denton Way. Then take the wide path due ish north (schools both sides) and cross over Langdon Road and along Rogerson Terrace. Go right into Stamfordham Road and at roundabout go up Newbiggin lane.
After half a mile turn left into Newbiggin Lane and immediately right up Hareydene. At top join cycle path heading west then north over the A696. You are now in Woolsington, so when the cycle path ends, as, sadly, they all do, turn left and follow the B6918 for a mile and a half to the airport.
