A base in a volcano. It speaks for itself, really.
A good top secret base needs to be really hard to access. Active volcanoes are a very good way to do this, as the constant supply of tons of lava make for a good defense system (except for the inhabitants) and source of energy. Said volcanoes are also more than likely to be in such inhospitable places as Mordor or a remote island. As well, the fact that volcanoes are attached to the earth makes an Elaborate Underground Base all the more easier.