Depends how far you want to go and where you start from [lots to see without using car?]
1. Cycle from home out to Hexham via Ovingham + Corbridge then back on south side through to Gateshead and home- lots of extensions to make it longer]
2. From home out to Tynemouth on C2C route along from Quayside, up to St Marys then back via Route 10 on Reivers Way to Ponteland, down to Newburn and back onto C2C along river home again.
3. From home down to Quayside, follow C2C in reverse out to Blaydon, following Derwent Walk up via Rowlands Gill to Consett and Waskerley Way- out to Burnside Cafe and back via Sunderland route, up coast to South Shields then back through Cycle Tunnel to North Shields and home following north bank of Tyne on C2C route to Quayside.
4. Follow C2C to Tynemouth then Coast and Castle [Route 1] up to Alnmouth and back or up to Berwick [then cycle back-110miles or train home].
5. Google Northern Rock Cyclone and print out maps to follow 62 or 100 mile route. Or use part of route and divert up to Rothbury.
6. Car to Keilder and cycle round it.
I'm still finding roads and tracks that I haven't seen before- I like the route up to and around the roads and tracks at Burnside Cafe best because of the views out over the moors beyond Consett.
Maybe see you out and about!
Chris