The monetary aspects of the L.I. list interest me.
First, even the more prestigious clubs were prepared to disclose their joining fees / annual subs / visitor fees.
Second, even after allowing for inflation, the member/guest costs are modest by modern US standards. For example, the more expensive joining fees were in the $100-$200 range and the most expensive annual subs were in the range $100-$150 (refer Garden City, Lido, National, Nassua, Shinnecock). To equate those numbers to today's money, you'd get a fair indication by simply multiplying by 100 (see below for reasoning). That suggests it cost something like $10,000-20,000 (in today's money) to join a top L.I. club in 1916, and then $10,000-15,000pa in subs: the fabulous Lido would have been at he top end of this range; membership at the National cost less than half as much; and a more modest private club substantially less again...
As context, the US had not entered WWI and the US economy was growing soundly at the time (ie the US was not in a state of economic distress nor military mobilisation in 1916).
[Maybe my numbers are a bit high or a bit low. There's no simple way to say what a dollar in 1916 would be worth in today's money, but the following indicative measures suggest a multiplier within the range 20-110 is not wholly unreasonable:
Since 1916 the average pay rates of skilled workers in the US have increased by roughly 110;
Those of unskilled workers by around 75 times; and
The US consumer price index is around 20 times higher than it was in 1916...
Back then a Model-T cost $360 & a ride on the NYC subway cost 5c]