The Donkey Kong Land Manual on page 16 states Big Ape City aka Big City is the same place Donkey Kong(Crank) used to stomp around. The characters get travel there from the Kong Archipelago by blimp.
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In Donkey Kong 94, Big City aka the location where Donkey Kong Arcade took place; is revealed to be on the same planet as the Mushroom Kingdom. Something even Miyamoto pointed out in a developer interview.
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