First, it depends on what you mean by "club", since the earliest things which are usually called SF clubs were science clubs whose members also liked SF. Do they count? If the bulk of the club's activity was sf-related, they would seem to be legitimate contenders for the title, but from when? It seems likely that when they were founded, they were founded as science clubs and over time sf took up a larger fraction of their attention. If so, do you count them as sf clubs from their foundation (clearly wrong) or from the point where sf became a majority interest (unknowable)? It's also worth remembering that in this Gernsbackian time, even a club which considered itself to be an sf club, would still discuss science a lot.
Secondly, the evidence is very unreliable since everyone involved is now dead and fanzines were invented later, so there's little or no contemporary documentation available.
The claim of the Eastbay Club is based on claims by its founder, Aubrey MacDermott. (See Aubrey MacDermott on the Origins of Fandom for details.) He holds, essentially, that his club was ignored by the New York-centric Fan History Establishment. This is not implausible, but it remains true that the evidence is entirely testimony of an interested party. Additionally, MacDermott is accused by some of "remembering" new facts when needed to retain his claim to primacy. (See letter from Fred Patten in File 770 #15 p23 .)
Between the vagueness of the question and the unreliability of the data, it seems unlikely we'll be able to resolve this, though the Scienceers seem to have the strongest claim.
Very Early Clubs:
|SCC/ISA||early Spring, 1928||Discounted by most fanhistorians as being mostly a science club.|
|Eastbay Club||April 1928||Unfortunately, the supporting evidence is not very strong.|
|Scienceers||December 11, 1929||The Scienceers has long been held to be the first club.|
|Boys' Scientifiction Club||1930||Supposedly formed by Ackerman because he couldn't travel to the Eastbay Club, but, if so, it doesn't seem to have been very large or very active.|
|Ilford Science Literary Circle||October 1930||The first club in the UK|
|Fan history||Reasonator Search|
|This is a fanhistory page. Please add more detail.|