Crestfallen Studios

I've just done the section in Reflective Sky where you get the mine key, so you can get into the tower.

Despite passing the building earlier, where do I need to go next?

You have to go back to the lost city area(The screen before Altair Mansion) and you can enter the houses in the north part of the area, which has a elevator in it that brings you down to the minds.

It might also be a good idea to do some of the sidequests now if you havent done them yet.