Sean,
I've played Silloth, which is absolutely first class.
It's quite beautiful, as well as having any number of first-rate holes, with only one or two around the turn a little ordinary.
Don't miss it. Seascale is in another, slightly harder to get to part of the Lake District, and is a little 'scruffier', but there's some terrific stuff there too, I think. 3,4,6,7,9,10,14,15 and especially 16 are all great holes to play. Super friendly members and staff,too.
You can even play on a Saturday for the unbelieveable bargain of 27.50.
I've played Southerness, and, in some ways, it reminds me a little of Harlech. Flattish, all long fours, five par threes and a solitary par five, but I think it's a better course.
As Mark R said, it's quite a lovely setting, a little isolated and off the beaten track, friendly staff, nice little town, all of which adds a little extra to the experience, and help offset it's relative blandness, but there are some good holes.
Well worth the visit if you are up in the Lake District.
I did quite like Burnham -it's a fairly inspiring place to play, I just thought a few of those holes around 7 and 8 were a bit plain, but some lovely stuff there. 9 is brilliant, equal of 17, I thought.
Strangely enough, on my recent trip back to the UK, all of the courses I played, from memory, had a first tee perilously close to the amused faces in the club bar, whereas I can't seem to remember those from my previous trip being so horrific.
For a first tee experience, you can't go past Southerndown, though. Tee shot straight up the Matterhorn, five feet from the clubhouse window, and, most likely, several woolly four-legged creatures occupying the rest of the tee.
Neat course, too.
Hope you get to play Machrie and can give us some feedback.