There is a half decent place in Whitburn itself.
If you go out towards Blackburn, past the hillcroft into East Whitburn, then turn right onto hens nest Road, follow this until the side pavements stop just past the houses, there is a small lay-by on the left, this is a public footpath, follow this into the woods, there are several routes, but keep going up the hill. Go to the top locally know as 'pet cemetery' 55 degree 51' 47.5"N 003 degree 38' 50.41"W.
There is a park style bench and a flat area which is fairly solid, there are trees to the north, but it has an elevated position looking to the South, East, and West.
It is usually good for the geminids and the other meteors around this time, and is ok for an early sight of the conjunction, it's a bit of a walk but reasonablely dark, not as good as a drive-out type site of course, but just a few mins from East Whitburn, depending which side of Whitburn you're at, just a few minutes as well.
It's a dark trail, so go during the day to get your bearings