When shopping for cycling shoes, look for:
A stiff sole: Stiff soles boost leverage on the pedal and decrease foot fatigue.
A good retaining system:
Laces, Velcro straps or other retaining systems hold your feet securely
in place, which aids the upward movement of your pedal stroke, and lend
stability by reducing movement.
Riding indoors generates considerable body heat and sweat, so make sure
the shoe features mesh or another breathable fabric that circulates air
to your feet.
Most road cleat systems have large protruding cleats that can make
walking difficult and hazardous in a gym environment. For Spinning
classes, your best bet is a shoe with a recessed cleat or SPD® (Shimano
Pedal Design) system and a rubberized sole for safety.