this isn't near Alnwick - by any stretch of the imagination - but its a nice option if you're coming from the west.
http://www.ukcampsite.co.uk/sites/reviews.asp?revid=6984
good views, quiet, easy access from the M6/A69, excellent breakfasts, and dark as fcuk if you like watching the stars. Hadrians wall is at the back of the farm...
E2A: the only place i wouldn't recommend is the FC site at Keilder - its lovely, but the midges are out in force, and in numbers to carry off small children or eat cattle in one sitting. go there in early Spring, Winter or late Autumn, but not now...