To vary the sensitivity of the light meter you have just made, try changing the value of the factor (57) that you divide the analog reading by.
Increasing this value will make the reading less sensitive.
Another thing that you could try is to change the sketch so that while the reading is below a certain level, the LEDs are on, but they automatically turn off when a threshold is exceeded. So putting your finger near the photocell to cut out most of the light will turn on the LEDs.
Simon Monk is author of a number of books relating to Open Source Hardware. The following books written by Simon are available from Adafruit: Programming Arduino, 30 Arduino Projects for the Evil Genius and Programming the Raspberry Pi.