To get more range out of an LDR, I use two or three resistors to power the LDR. The resistors are connected to outputs of the Arduino. One output can have a 1k resistor and one output can have 100k resistor (or even more).
I power the outputs one by one, and average the result. With that, I can see the difference between a dark night and a night when the moon is shining.
I don't use such modules, and because of the high value of the 100k resistor, it needs to be close to the Arduino and I use delays before taking a sample with analogRead() and I do averaging of a number of samples.
This schematic might be the one:
