Most chess clubs in my area struggle to gather more than 30 federated members with only one club past the 100-member count in a territory of 8 million people.
Which is the largest physical chess club in the World and how many members does it have?
According to the French Chess Federation, Marseille Échecs is the largest French club, totaling 831 officially registered players.
Two other French clubs have more than 500 members, in the cities of Bois-Colombes (612) and Villepinte (584), both near Paris.
Located in Hamburg, second largest city of Germany with a population of approx. 1.8 Mio people. The number includes younger players, partly without national rating number. In Germany there are about 60 clubs with more than 100 members. Interestingly, to my information no club in Berlin (which is 2 times bigger than Hamburg) comes anywhere near the member count of the Hamburger SK. On the other hand there are 17 clubs in Berlin to choose from.
(The Mechanics' Institute Chess Club in San Francisco)
This just based on the size of their staff, their membership fees are relatively low, hours of operation, and that it is the oldest chess club in the United States; Zurich has the oldest club.
That said, I was unable to find any chess club that post yearly counts for membership purchased and/or given; that said, games played onsite, and the average rating of those games would likely be a more useful numbers.
UPDATE: So, according to John Donaldson, Chess Director of the Mechanics' Institute Chess Club, he guessed 250 players use the club a month; reason for a guess is that it's complicated to know the exact count, since the membership is to the Institute, not just the chess club. Also, he said that the Tuesday Marathon attracts roughly 100 players.
(Marshall Chess Club, New York, NY)
Roughly 500 "active" members; meaning the player's membership is currently paid in full. It's free to visit one-time, and there's blitz games on Friday for players of any rating for $20.