Emerald Cave of Origin
The sacred cavern beneath Sootopolis, said to be where Hoenn's weather first stirred. In Emerald the great beast that slept here has moved on, so the bottom holds the storm's eye, not a catch.
Cave of Origin is in Hoenn. In the story you arrive from Sootopolis City to the south and it comes before Route 129.
CAVE OF ORIGIN MAP
The Cave of Origin is one long ladder chain down from Sootopolis with no puzzle to it, just the descent to the bottom and the climb back out.
Pokemon Encounters
Down in the Cave of Origin, Sableye is the catch to chase at 30%, lurking among wall-to-wall Zubat and Golbat in the mid 30s.
Zubat
Cave of Origin Guide
Because Rayquaza settles the fight instead. When Groudon and Kyogre clash here during the Sootopolis crisis, you bring Rayquaza in to break them up, and the two titans leave for their own hidden caves rather than sticking around to be caught. All that's left underground is the odd Zubat or Sableye.
Out in roaming weather caves, and only once you're Champion. A drought opens Terra Cave for Groudon somewhere on the map, and heavy rain floods Marine Cave for Kyogre. The Weather Institute on Route 119 reports which route the freak weather hit, so start there.
Almost never. You can feel your way through the dark stretches, and the cave HM that actually earns a party slot is Rock Smash, not Flash. Flash only matters for a couple of black rooms late in Victory Road, so don't waste an early move slot on it.
Yes, more than Flash is. Smashing the cracked rocks in Granite Cave turns up a Nosepass you won't meet any other way, and the ones in Victory Road hide Geodude and Graveler. Keep one party member who knows it so you're not backtracking when a breakable rock shows up.

