This token is from a German Gymnastics Club. The
German Club here in Brisbane, Australia has this same four-F-in-a-cross symbol, but I suspect it's just a coincidence. This club did make tokens, but only one type that I'm aware of, and it didn't resemble this.
If I am correct, then the "TV" on your token stands for Turn-Verein, which is German for "gymnastics club". The Turnverein movement was founded in 1811 and saw clubs founded throughout Germany and into the German diaspora, and many of these clubs seem to have adopted the four-F logo. The four "F"s stand for "Frisch, Fromm, Fröhlich, Frei." (or Fresh, Faithful, Friendly, Free in slightly poeticized translation).
Here's a website outlining the movement's history. The club in Brisbane is now just a social club and German restaurant, I don't think physical activity is part of their emphasis any more. It's not surprising the club's mandate has shifted from its origins, given that it was forced to shut down and hand over its membership list during both world wars.
So now, to work out where your token might be from, we just need to work out what or where "A A" might be. Presumably a place name, and somewhere with (historically) a significant German minority.
They still exist in America, and call themselves the "American Turners". Their
Website lists their active clubs, though your token may be from a club that's now defunct.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis