I found a Giant Spider dungeon up inside a mountain once, made a nice drop-to-kill string grinder out of it.
If you're trying to keep the Spawn area as natural-looking as possible on the surface, as long as you light everything up well with torches, you can bury just about everything you'd need to build underground, no problem. I used to build quite extensive underground bases inside mountains, and aside from a few entrance/exit areas and the odd skylight for old-style villages or beacons, I modified the terrain above ground as little as possible. And yes, these included darkroom-based mob/item grinders with a drop-to-kill mechanism (later supplemented with a lava blade once they started letting skeletons and zombies spawn with Feather Fall 4 enchanted armor).
And if you're building extensive underground facilities...you'll eventually break into most of the caves nearby anyways. Just make sure you loot and light them extensively and don't leave spawnable dark areas inside them. So the caves aren't the problem when it comes to spawning rates. Lighting up the surface with a crapload of torches is gonna be more of a problem, especially on uneven ground. And, these days, lighting up the surface includes the seafloor and riverbeds due to Drowned.
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