Every surface serves your need. We touch only surfaces - 2nd D objects. Even our eyesight wors only in 2 D - 3D is only brain interpretaton. Informational organization on retina is just 2D. The surface of a computer or TV set screen is just 2D, no more. We acually live in the 2D world arranged in the 3 D space.
I suppose this depends on your philosophy. An engineer would be satisfied calling something like paper two-dimensional as long as it can be accurately modeled as a 2D object. If you are pickier about the details, you will struggle to find a 2D object in a 3D world. I like the shadow answer.
The wave front of transverse electromagnetic wave is a 2 dimensional object or surface . Take any decent book on electromagnetic theory. You can feel it directly when you take ,for instance ,a sunbath.