An interesting question ...
When I first played my club, Royal Colwood, I remember thinking as I played #6 if I ever joined a private club it would be there.
First links I ever played was Royal Cinque Ports. I walked the course with a friend the day before we played for the first time and we were literally giggling in anticipation of playing it. A few others:
Royal Dornoch
Royal County Down
TOC - it doesn't live up to some players' expectations, it exceeded mine and has continued to do so every time I played it.
Macrahanish - still the most FUN ever playing a course
Bandon Dunes - heard about this real links course in North America and played there the year it opened,
Pacific Dunes - another course at Bandon and as good and as unique as the first
Jasper
Riviera - greatly anticipated, not disappointed. And even though I had admired and studied #10 from afar, the real hole was sublime, better than I thought.