I don't typically make stripmines, I just go deeper into my cave base, or find one nearby. Somehow I still end up with lots of stone though... I would build with stone more often but I don't have the patience for it, and wood is just easier to get.
When I don't live in a mountain I just make a wooden base in a plains which I will soon turn into a forest, or sometimes I forcefully impose my dictatorship over a village by building a fence and a huge tower, the more imposing the better.