I'm a physics professor who regularly teaches about special relativity in my Modern Physics course. I've made a web app for drawing spacetime diagrams (technically, two-observer Minkowski diagrams), which are one of the best ways I know for building intuition about how relativity works. The link points to an introduction to the diagrams, including a brief explanation of some key relativity concepts based on diagram illustrations. (It's meant to be at least halfway understandable to people who haven't studied physics before, though it'll be clearer the more you already know.)

Read through the linked page if you want the basics, or if you're eager to just jump straight in, follow the links to use the main app and play with that. (It has multiple predefined scenarios that you can load, each with a brief explanation, but you can design your own scenarios as well.)

[Aside: I feel really good about the UI I've got for this so far, but my last significant JavaScript work before this project was back in 2005 or so. I've had to learn a LOT.]