In the game I’m making, I’m going for a stylized look for it that is similar to Killer 7. Essentially, I want the shadows to have only a certain number of levels to it, as seen in this image https://i.ytimg.com/vi/7XquUe99t6Y/maxresdefault.jpg most notably on his face. Do I do this through code, or do I do this through a texture?
Yes, you use a toon shader with a discrete gradient ramp - Unity’s own Toon-> Lit shader will do as a start point. Here’s a useful article with more detail: Next-Gen Cel Shading in Unity 5