I think Myopia, Chicago, and Garden City were all Landmark courses, but their influence was nothing like that of NGLA. NGLA changed the entire approach to golf design across America.
The timeline of NGLA was misleading because they originally planned to use a local in instead of a clubhouse, but the Inn burnt to the ground. The club was not officially open until a clubhouse could be built and opened in 1911. But they were golfing in the course in 1909 and the first tournament was held in 1910.
I'm doing this off the top of my head, but I believe the timeline for NGLA is something like this
1901 - Motivated by the best and most difficult holes discussion in Golf Illustrated, CBM came up with the idea for NGLA.
1902 - CBM traveled abroad to further study the great courses, with the idea of bringing them to the US.
1904 - The charter members agree to a general approach to creating the course.
- Second study trip abroad.
- Articles begin appearing nationwide about CBM's plan, and a debate/criticism begins in the British press about it.
1906 - Third study trip abroad.
- NGLA land secured (by option allowing for much flexibility in the exact final specifications) after Whigham and Macdonald ride the site and find a rough routing. (This set the best practice for creating a golf course)
- Planning completed and construction begins.
- Discussion and debate continues.
1907 - Construction finishes and course seeded.
1908 - agronomy problems delay opening, some (all?) greens and turf reseeded .
- Shinnecock Inn, which was going to be used in leau of a clubhouse, burns to the ground.
1909 - First play on the course, work and refinements continue.
1910 - Play continues, first tournament, work and refinements continue.
1911 - Clubhouse completed, and tournament held for the "official" grand opening of the Club. CBM still reportedly tinkering well into the 1930s.
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When I look at the significance of these early courses, I try to put myself into the mindset of those there, and figure out what they thought was significant and try to look at the influence various courses had. Myopia, Garden City, and Chicago were all considered good courses, for America. But among those who knew both, they generally did not compare favorably to the great courses abroad. NGLA did.