The best place to meet would be the junction off the A1 signed 'Morpeth North' (so the person coming from the south will go past the Morpeth junction) where the A697 from Wooler joins the A1 and comes into Morpeth. Take the signs for Morpth town centre, then on your left you'll see the Fairmoor garage, also a vet's and a country store (was Farmway but might be Carrs Billington now?). it is just a wee garage, but there should be enough space there to get sorted out (not really anything big and obvious in Morpeth.
Another alternative could be the Heighley Gate Garden Centre, just about a mile back up the A697 out of Morpeth towards Wooler - they have a HUGE carpark. You'd also get very nice (and expensive) coffee and cake there.