What was the first city to have installed lighting?

If you are talking about lighting in a city street, the answer is Cleveland, Ohio.

Street lights or residential lights?

The first city to have electric street lights was Godalming, UK (1881).
Street light - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Street_light)

Residential lights is more vague, about the same time some landmarks in england got interior lights
Incandescent light bulb - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Light_bulbs)

The first electric street light were developed by a russain called Pavel Yablochkov and they were first used to light de louvre in paris where 30 were used they were electric (carbon Arc ) but they still burnt down the first town however to use hardwired electrical street lights in a grid format as we do now was Godalming in the UK in 1881 hope this helped ( no doubt with a homework assignment lol )