Where are the slaughter arenas?

There are 2 normal slaughter arenas in the game (bandits & Hyperion robots) and 2 DLC arenas (wildlife, and fantasy).

The first one, the bandit slaughter arena, is accessed from the Fridge (which you'll be heading to very soon), just inside on the left. The Hyperion slaughter arena is in the Ore Chasm, which is reached from the Eridium Blight (one of the last areas you'll go to). If you have the DLC for the Creature Slaughter Dome, that's in the Natural Selection Annex which is accessed from the Wildlife Exploitation Preserve. There is also a Fantasy-themed Slaughter Dome in the fourth campaign DLC, Tiny Tina's Assault of Dragon Keep, in the Murderlin's Temple area.