Building a good-looking case does not need to be hard. In the hands-on chapters of this book (Chapter 5, Building Your Own Automatic Pet Food Dispenser, Chapter 6, Building a Smart E-Ink To-Do List, Chapter 7, Building a Smart Productivity Cube, Part 1, and Chapter 8, Building a Smart Productivity Cube, Part 2), we built all of the cases from scratch using cardboard. While this gives you a lot of flexibility, it might take more time than you are willing to spend for your next Arduino-based project.
A great starting point for custom-built prototype cases are household boxes or boxes that you can buy in arts and crafts stores. Most prototypes live in a rectangular box anyway. Why not use an existing one and put in the holes needed for your user interface, cables, or display? Using existing boxes also lets you re-use boxes that might go into the trash...