Bring your own cup!
Although paper coffee cups seem like they would fall into the same category as juice boxes or milk cartons, they belong in the garbage. The paper cups are coated on the inside of the cup with a material called polythene to keep the contents warm. Even though polythene looks a lot like the wax coating on your traditional milk carton, it binds more tightly to the cup making it very difficult to recycle.
Instead, grab your own travel mug and ask the barista to fill it up. Many coffee shops even offer a discount for those who bring their own cup!