Why not incorporate G, C, and A into a logo a la the Hartford Golf Club logo (or any other club whose initials are superimposed on one another to make an emblem)? It would be good homage to the classic golf courses.
Hartford GC's emblem has a wide G, a tall C which intersects with the G, and the H, which encompasses both. Of course, we could put the A in the middle, its three points ending at semi-symmetrically prudent spots in the C (meaning a tall, narrow A) or the G (meaning a short, wide A). I think that it would better to have the G be tall and narrower, as it's the first letter of the acronym, and the tall letter is the one that draws one's eye first.