First mountain area I encountered near my spawn-- It's slightly separated from another large mountain biome by a little stretch of forest and river. The mountains are full of little tunnels and hidden passages and cave entrances, there's also a small ravine in here that goes into a cave system.
Coords from somewhere in the middle of those mountains: x:269 z:405
'Coliseum Rock' on the edge of that range,
travel approximately due west from there to reach a ravine that drops you to level 13 and has multiple 'floors' and side caves
Extremely steep, narrow canyons in this other mountain range area