There's a great line just posted by Michael - 'Just analyze the golf course itself, nothing else.'
In a different post recently I used the phrase 'it's the view not the course' about a certain 2-course location on the west coast of Scotland which has hosted The Open a few times and has a smart hotel on a hill overlooking the sea and two the courses and from which you can see an island famous for quarrying curling stones. Yip, the Ailsa at Turnberry. Great location? Yes. Great views? Yes. Great course? Um?
Now, consider the Championship Course at Carnoustie. Great historic Open venue? Yes. Course tough as old boots? Yes. Great Location? Um. Great views? No way!
If you 'just analyze the golf course itself, nothing else', and you picked up the Ailsa course at Turnberry and dropped it next to the railway line in the wee grey town of Carnoustie, would many people visit there to play it? Um, I don't think so somehow.
On the other hand, if you took the Championship Course at Carnoustie, picked it up and dropped it on Turnberry's stunning location on the west coast of SCotland golfers would flock there, like flies to a dung heap IMO.
Whilst the overall ambience of the club is an essential element, and this includes all kinds of factors including the location, clubhouse, facilities, views, terrain, history, PR friendliness, lay-out, designer, what tournaments/championships has it hosted, if you adopt the criteria of 'Just analyze the golf course itself, nothing else' then I suggest you might achieve a different outcome in terms of 'greatness'.
Hence there are only two 'greats' for me in the UK, namely Muirfield and Carnoustie - the other Open venues and other premier UK courses are IMO in a tier below these two - perhaps one of the heath land courses west of London might make it three in my top tier but I can't include in my list somewhere I haven't (yet) played.
All the best.