What cave do you go to see the adamant and lustrous orbs?

You're likely thinking of Mount Coronet in the Pokémon Diamond, Pearl, and Platinum games. This mountain holds both the Adamant Orb and the Lustrous Orb, which are used to evolve certain Pokémon.

However, you don't actually enter a "cave" to get them. You find them in:

* Adamant Orb: In the Peak of Mount Coronet near the top of the mountain.

* Lustrous Orb: In the Summit of Mount Coronet which is a separate area you reach after completing the game and accessing the post-game story.

So, while you're not going into a specific "cave", you'll be venturing through various areas of Mount Coronet to obtain these orbs.