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Sorry for the quality of the image but allow me to go somewhat in-depth.
First of all, this gym would be your means of transportation to the next area as it would be taking place on a blimp.
It would be a rather large blimp so there would be some sort of elevator puzzle where you run into gym trainers disguised as fellow passengers, and after you find the correct path there would be a red elevator labeled with a bright red.
"Captain and challengers only from this point."
And finally you would be met with the gym leader, on top of a blimp and there is a constant airlock/delta stream effect going on for this battle as the blimp is in motion.
Also the badge would be called
"The Glide Badge"