Not sure if this has been mentioned, but a very nice way of finding deep underground caves with little effort is to set the game to hard, gather up a stuffload of pickaxes and torches, then go out wherever you want to dig then just dig straight down. After you've gone down a bit tap F really fast to change the view distance, and look around the skybox (better to do this at day so it's easier to see) and look for dark figures (monsters). Once you see an area with tons of monsters in it, dig towards it and then once you're close to it change the difficulty to peaceful (unless you want to fight the stuffloads of monsters) and just dig into the cave. Been doing this for a while and it works well.
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