From Tweed Green, follow the path upriver past the swimming pool and through Hay Lodge Park. Continue past Neidpath Castle.
When you come to the viaduct, either continue under it and join the disused railway a little further upstream or climb the steps and continue West along the disused railway line.
Cross the river when you reach the bridge over the Tweed and turn left towards the old manor bridge (c.1702). Stop for a while to enjoy the river at this point - before continuing up hill.
When you approach the brow of the hill, you can enjoy views behind and in front.
From here, you can either follow the path through the fields to join Caledonian Road or stay on the Sware road and follow it round and back into town via Edderston Road.
This route can, of course, be enjoyed in reverse.