I really liked the set of threes on the New Course:
#5 - Kind of secluded atmosphere in a bowl surrounded by gorse - the classic table top style green with the weird drop off that cuts into the green on the back right
#9 - Awesome uphill hole along the Eden. Blind over a little ridge at the front that leads to great anticipation as you walk up the hill to see where your ball ended up (and it precedes #10, one of my favorite holes anywhere)
#13 - Green benched up along one of the higher dunes - very interesting set of options as to how to get the ball to sit on the green without leaving an ugly downhill chip from over the green.
#17 - I kind of consider this a candidate for a template on a firm site - long hole with a bunker short asks the question as to where to land the ball in order to get it to stop near the hole - the open nature of the land opens up some uncertainty about the distances required - I found this hole very challenging while using very few architectural tools to accomplish it (short bunker and general lack of definition)
For some reason the New Course kept popping into my head as well, mostly 9 and 17. The 9th might be the most "natural" hole out on the Links with no revetted bunkers and marram and wispy fescue growing into the hummocks and hollows leading into the green, though that growth only adds texture and doesn't prohibit run-up shots.
The 17th would be my nomination just from personal experience and circumstance. For the conditions I played in during my 3 day ticket in September (very fast turf, medium strong westerly wind), it plays as one of the best par 3s I've ever played. The fronting bunker was in the exact place I wanted to land my ball. Since it was a 3 day ticket and I was playing until moonlight, I had the opportunity to test it and prove it true. Awesome challenge and fun. I did play again that following winter with calm conditions, and the bunker was not as much an issue. Fortunately though, the prevailing conditions on the Links are much more like the former.
Other holes that are popping into my head without thinking too much are the 2nd at Kingsbarns, the adjacent one shotters on the Eden, the 2nd at Elie, and the 11th at Askernish if every running ball on the left didn't shoot down the road.