Pokkén Tournament offers nineteen battle stages on Wii U, all located in the Ferrum region. Eight are available from the start; the other eleven are unlocked in the Ferrum League. Here is the complete list, with how to obtain them.

Stages available from the start

StageIn a few words
Ferrum StadiumThe stadium of the Ferrum League final, by a lake, always packed with spectators
Old Ferrum VillageThe “city of water,” with its park, its arched gate and its clock tower
Mountain VillageA mountain village where Ferrum battles have long been held in the square
Phos VolcanoA cave in the heart of a volcano, between synergy stones and ancient ruins
Diggersby LandAn amusement park celebrating Diggersby, in three zones
Ferrum DojoAn ancestral dojo, in a spring, summer or winter version depending on the draw
Training RoomAn exercise room, in a Speed or Power version depending on the draw
Neo City (day)The biggest city in Ferrum, where humans and Pokémon live together

Stages to unlock in the Ferrum League

These six stages are obtained by fighting a battle there during the Ferrum League:

StageIn a few words
Neo City (night)The big city under the neon lights, reflected in the puddles
Old Ferrum Village (winter)The village under snow, during its sculpture contest
Mountain Village (autumn)The mountain village in autumn colors, with Sawsbuck and Deerling
Haunted HouseAn abandoned mansion, lair of Ghost-type Pokémon
Mystery CarnivalA forgotten mansion where a party is going on with nobody there
Magikarp FestivalA fishermen’s festival on a boat, where Hariyama waves a flag

The story stages

The last five are unlocked by progressing through Shadow Mewtwo’s story, by winning the corresponding battle there:

StageCondition
Regi RuinsDefeat Glenn there during the main story
Blue DomeDefeat Nora there during the main story
Dragon’s NestDefeat Jake there during the main story
Black ColiseumDefeat Shadow Mewtwo during the story
Black Coliseum (final)Defeat Shadow Mewtwo and complete the story

The arenas differ in their scenery and size, which changes how you play in the Field Phase a little. Our article from the time, Battle stages, gives the size of each one. The DX version adds two, including Thalia Beach.