Just got back from a trip there a few weeks ago
I'd add Western Gailes to the mix even though I haven't seen it mentioned yet: http://www.westerngailes.com/
It's a textbook definition of a classic links course. They don't have the facilities to host the larger tournaments (i.e. driving/practice range) so they don't get the same press or coverage as some of the other courses like the Dundonald which is right next door and just hosted the Scottish Open. But, if they were able to make some property appear out of thin air and add those facilities, I think they would be hosting some bigger tournaments left and right. The greens are technical and you'd be tested on a lot of approach shots. The holes change elevation and each one would face a different way in the wind so it feels like a different course on each hole.
1.) Old Course has to be on there for the history, the jitters you get for being/playing there, #1 & #18 in the city square, Swilcan Bridge, the road hole, the double greens, the number of people that will be on the course whether playing golf or locals walking their dogs/taking a family stroll if the weather is nice, the R&A building staring you down, people enthusiastically cheering for putters on the 18th, and the chance to play a hole with blind bunkers that were designed to be played from the opposite direction. So, for the experience/history of it, not because I'd be looking for a technically great golf course. I got to play this 2 times from winning the ballot process and because we had our names on a cancellation list before that.
2.) Kingsbarns - awesome, public, North Sea views on every hole, looks like it's 100 years old already even though it only goes back to the 90's. Everywhere you turn your head is a postcard view. Fairways are fairer to the less than stellar golfer because they feel a bit wider than a lot of the other courses. I had a great caddie here so that really helped my experience here.
3.) Carnoustie - you get setup for sadness when you're playing the front 9 and thinking "heck, this isn't exactly easy with the wind, but, it isn't nearly as tough as everyone makes this out to be.. Car-Nasty ... psshhh yea right.." then you'd get to the back 9 and remember why you have a desk job and would go hungry and homeless if you tried to play professionally. You get to play Hogan's alley, try to get a par on a hole to beat Tom Watson and try to stay drier than Van De Velde all within one round.
4.) Western Gailes - for reasons noted above.
5.) Prestwick - home of the Open, Tom Morris Jr.'s Claret belt, and blind tee shots. A historic course designed for old school golf. Some of the greens are still original to when Tom Morris was the keeper of the greens. Blind tee shot that would leave you thinking "Old Tom Morris really had quite the imagination when he came up with this one..." then you get to ring a bell saying you're group is clear of the green - assuming you make it past #3's Cardinal bunker and the narrow fairway on #1. Biggest drawback - right next to the airport)
I played all 5 above so they make my top 5 out of bias and good memories. If I'm ever lucky enough to go back, then I'd love the chance to play these ones.
6.) The Royal Troon - heard a lot about this course from a few locals who enjoyed it quite a bit or were members.
7.) St. Andrews Castle Course or New Course (a lot of locals mentioned that they liked the castle course quite a bit, so, I'd like to see what that was all about - most people have said that the New Course is better golf-wise than the old course - I'd also like to compare just for giggles)
9.) Royal Aberdeen
10.) Kings Course Gleneagles
Tips if you're thinking of going:
1.) If you're back and forth on pulling the trigger and making the golf trip happen, you're nuts, just do it.
2.) If it's worth doing, it's worth doing right - get a golf travel company involved to help you book tee times and get on the ballot where you want to play. If you choose a good one then they might have some pull for helping you get some tee times, etc. We used Premier Golf and I would use them again in a heartbeat. Also, get a van/driver hired for the duration of your trip - pays for itself in convenience and can really pull the trip together because the last thing you want to do after getting your butt beat by some of the courses is drive back to the hotel on unfamiliar roads and on what could be the opposite side of the road for you - let someone else deal with that - they also might just have some killer local knowledge like what places to hit up for food, pubs for drinks (*cough and then having them drive you home from the pub cough*), history of the area, and generally great comradery - we had a driver & we ended up inviting him to come to dinner with us because he was fun to hang out with.
3.) Considering requesting caddies? Do it. local knowledge makes the course much more enjoyable, the help on the greens is pretty nice, not having to carry a bag every day isn't overrated, I would have had no idea what club to hit into the wind on a solid chunk of the holes, they are hilarious, very personable, and some even have great tips/golf knowledge/skill that they will share with you. Don't forget gratuity on top of normal caddy fees.
4.) Umbrella - lol, good luck, it comes down sideways... just pack your rain gear/suit.
5.) Extra balls? Pack them, then add another box - heaven forbid, you hit it into the wispy grass, a good caddie will be able to help you find it, but you will have holes where you're just out of luck because the growth/heather/gorse is just that dense.
6.) go with 7 of your buddies and rotate the foursomes for each round to mix it up a bit and have your bonding time rotated amongst your group.
7.) Try playing and tracking the week using a point system based on everyone's handicap - makes the trip fun and more engaging for every player - including the higher handicaps - keeps them engaged and excited for the next course.
8.) if you're flying in from across the Atlantic, play a slightly notable, but less than amazing course to begin with if you're given the choice. You're going to be jet lagged from taking a red-eye and landing in the morning -just skip the hotel, go straight to a golf course and get that first round out of your system. You'll be a zombie on the front 9, but your body will start to wake up again on the back 9 (even if all you want to do is take crash and study the back of your eyelids).
9.) If you arrive but your clubs don't - forget about waiting for them, you're in Scotland & they might not show up for quite a while - buy or rent the stuff that you need but got left behind, now isn't the time for a Marine mentality forget about it and try to move on/enjoy your trip.
10.) Budget the crap out of it so you can spend money on the things that will make your trip easier, more comfortable, or more memorable. If you're like many, then it might be the only time you ever get to do a trip like that - do it so you don't have any regrets when you get home or at least try to minimize them.
11.) Have a group link sent out for an online file sharing platform like Box or Google Drive so that everyone can upload their photos to the same place. You're making awesome memories, try to capture as many as you can & be good about sharing them with your group. Also, consider an international plan for your phone for data & using something like WhatsApp as a group messenger system so you all can communicate while youre over there/talk to friends/family back home about how awesome of a time you are having.
12.) budget for the golf-bug when you get home - it bites hard and turns out to be highly contagious. Side effects include justifying the club(s) you really wanted to get before your trip, greens fees, and driving range parking lots.