In urban areas, rain at night means great photography. The streets glisten and reflections are awesome, and I encourage you to brave the elements and take pictures. If you are dealing with a hard rain, then obviously this is not conducive to shooting. But if it's a very light rain or a drizzle, bring an umbrella and a plastic cover for your camera and look for beautiful images of buildings and neon lights reflecting in the wet streets.
The photo above is the old square in Krakow, Poland. This would be a very pretty night shot at any time, but with the light rain it was esspecially beautiful. Use a tripod, a low ISO like 200, the mirror lockup feature and either a cable release or the self-timer to eliminate camera vibration. Also, carry a microfiber cloth to wipe the lens of rain drops.