September. In January, the early birds of the Tucson Gem and Mineral Show are flocking in. February the shows are in full swing and in the Fall a smaller version that is gaining in popularlity appears.
In September, there's a smaller show but one that is gaining attention and traction.
Keep in mind, this is really a combination of multiple shows across Tucson starting in mid-January and continuing thru mid-February.
From the TGMS.org website: "The largest, oldest and most prestigious gem and mineral show in the world.
The Tucson Gem and Mineral Show® has enjoyed international stature since the 1970s, and was the first gem and mineral show to bring the hobby enthusiast, the public, and the curator/professionals together for discovery and discussion."