How to create a "cartoony" texture, like in Subway Surfers?

You can make or import a specific shader (toon shader with special shadow ramp) and apply them to each game object mesh ( system use in mobile) or better you can apply one post process filter effect directly into the camera that transform the final image into cartoony style.

Toon Shaders: In the Standard Assets, effect folder, there is a toonShading folder including ToonBasic shader, ToonBasicOutline, ToonLit and ToonLitOutline. I think you must download the "Shader Calibration Scene" from the asset store for getting this free Unity shaders examples.

Filter Effects: It apply a filter to the final rendering image (more computational cost). Probably you want to use les color transitions sfumature and less number of colors (16? in tot) in the pallet so that the shadows are hard and the surface looks like plane. In the filters you can add a border to the edges.

Look into the asset store in shaders and post process effect filters as reference to understand the effect you are looking for. You can active them using the Unity plugins and making same trim in it. Or making script shaders. There is a nice book about scripting shaders and includes scripting examples of toon ramps.