Richard
I assume that you are staying over in Carlisle on the way up ?
If so you may want to start the day with a game at Carlisle GC. I haven't played for several years but I always enjoyed it when I played there. Laid out in 1936 by Dr MacKenzies brother Charles with input by Theodore Moone. MacKenzie Ross later did some revisions (according to the club website) and I think also Pennink/CK Cotton (not on the club website). From memory there aren't any real clunkers and a lot of very good holes, in particular a short par 3 which I really liked.
A few miles to the east of Carlisle GC is Brampton GC which is a Braid course. Good fun but also a bit up and down. If you are going to be playing a good bit of golf on the trip I'd opt for Carlise to save the legs and because it is basically a better course.
If you are then travelling north up the M74 before you cut across country at the A702 you have several courses "just off" the motorway. Lockerbie which I haven't played and not really heard anything about, Moffat which I also haven't played but have been reliably informed is an ideal course if you have one leg shorter than the other and like hill walking, and Lochmaben which I have played. Originally a 9 hole Braid course it has been extended to 18 holes producing two distinct nines. I played it a couple of times a number of years ago and I quite enjoyed it from what I remember.
Once you cut across country on the A702 the only course I've played is Biggar, which is the home course of Alfie and Harry Ward. It's largely a David Adams course from 1922 and is fairly inoffensive but nothing to write home about from what I recall.
Niall