There is NO volcano badge there's
Strition city-trio badge
Nacerna city-basic badge
Castelia city-insect badge
Nimbas city-bolt badge
Driftviel city-quake badge
Mistralion city-jet badge
Icirrus city-freeze badge
Opelucid city-legend badge
Mistralton City
In the theme park in Nimbasa City.
Coal Badge (Oreburgh City)Forest Badge (Eterna City)Cobal Badge (Veilstone City)Fen Badge (Pastoria City)Relic Badge (Hearthome City)Mine Badge (Canalave City)Glaceon Badge (Snowpoint City)Beacon Badge (Sunyshore City)
You don't. The city will return back to normal once you obtain the badge at Snowpoint city.
The Cascade Badge
Fortree City ( Feather Badge ) Leader's pokemon: Altaria, Swellow, Skarmory, Pelipper
viridian city
The third badge is in Goldenrod City.
It is the balance badge where you fight Norman(your father) in Petalburg City .
You get your 3rd badge in Veilstone city against Maylene.
the third badge in sapphire is at mauville city(north of slateport city)
vermillon city