I think it would be awesome if somebody made a 3D, first person computer game where the speed of light was significantly slower (perhaps 30mph as in the Mr Tompkins books) and did relativistically correct rendering so that you could see the geometric distortions and Doppler shifts as you walked around. It might be necessary to map the visible spectrum onto the full electromagnetic spectrum in order continue to be able to continue to see everything (albeit with reddish or bluish hues) when you're moving quickly.
It would have to be a single player game because (in the absence of time travel) there is no way to simulate the time dilation that would occur between players moving around at different speeds.
It appears that I'm not the first person to have this idea, though the game mentioned there (Relativity) doesn't seem to be quite what I'm looking for.
I do realize that it might be quite difficult to do this with current graphics engines, but I'm sure it could be done in real time, perhaps with the aid of suitable vertex and pixel shaders for the geometric/chromatic distortions respectively.