The loop Sven mentions is in Derek Purdys book, Broadstruther loop – Wooler common, hells path, broadstruther,Hawsen burn,langleeford, then back to Wooler via skirl naked.
From Alwinton heading up onto the border ridge and Windy Gyle is a good ride out, especially on the slabs at the top, loads of other bridleways up there as well.
Ingram to Linhope, then low bleakhope, Ewartley shank, Alnham, prendwick then back to Ingram is ok as well.