I would not be at all surprised if there are absolutely massive cave complexes deeper in the crust, but it's so bloody hot down there that it's nowhere you'd want to live. Even the deeper mining operations are at the boundary of a sustainable working temperature for humans.
Quickest way would be transporters. Unfortunately, the Enterprise won't be here for another couple of hundred years. In the mean time, I'm guessing doing what they all do, plane ride to the poles and entering.