Im looking for advice on how to be able to take one mesh (say a cube for example), and create a button that you could click on for each side (polygon face) of a cube. So if you take you mouse and click outside the cube it will rotate when dragging, and if you hover over a face it will glow or show some sort of section, and finally when you click on the side it will select.
Is there a way to do something like this without breaking up the mesh into individual pieces? Thanks!
Anyone? 
There are ways, like adding empty child transforms with box colliders.
but the mesh itself, no, not without breaking it into multiple meshes
(there is one exception: if you have a mathematical way to define the “area” you clicked due to the normal of the raycast hit or the sector of the models bounding box in which you hit - but to make this visually show something you must either dublicate out the selected part of the model, or use multiple materials on the object, one for each of these areas, to switch the texture there for example)
im sure you could do it, you will need to figure out a way to get the specific verts from the mesh object (or sharedMesh with modifying a skinned mesh) But as dreamora said, you will need a way to pick what verts you want to reference, then do what you need to do to it (rotate the cube, change its color, etc)