When you go to down the A1 to Northumberland, divert off to go to Coldingham and Coldingham Sands in Scotland, after the town itself there is a gorgeous little small cove and beach and there is also a very picturesque 20 minute walk which is above the cove/beach with good views that leads you to St Abbs which is a beautiful little fishing village, i know you could bike from one place to the other but the walk itself is stunning.
Also The Holy Island of Lindesfarne, is one of my favourite places on earth, tide depending, it's very popular with bikers as you probably know, i don't know how much actual walking you want to do, but if you fancy a walk while there make sure you do the Lindefarne to North shore walk, very lovely, you could also take the country roads around the Lowick area, some great country views.