I've never thought of a moonlight garden, but what a charming idea! I looked it up and some plants that flower at night include the moonflower, the nocturnal daylily, night phlox, yucca, and angel's trumpet.
I agree that it is a lovely idea. I wish I could do something like that as well, but it is not feasible with my set up. It makes me curious, though. Maybe I'll do some research on this, too.