How to amplify the resistance of LDR between 500-900 Ohms for use as Arduino input (0-5V)
The problem with your circuit is that the load resistor is mismatched to the resistance range of the sensor you care about.  The sensor in series with a resistor gives you a voltage that varies as a function of the full sensor range, from 0 to &infin;.  However, the resulution is highest in the middle of the range, which is when the sensor and the load resitances are equal.

Therefore the solution is to use your top circuit but make R1 640 &Omega; instead of 10 k&Omega;.  That also produces a low enough impedance signal that you can directly connect it to the A/D input of most microcontrollers.

With a 640 &Omega; load resistor you get 2.58 V at 600 &Omega; and 2.22 V at 800 &Omega;, for a 360 mV difference between the two light levels you care about.  With a 10 bit A/D, which is common in microcontrollers nowadays, that's 73 counts.  Many micros are available with 12 bit A/D now, which would get you over 290 counts, or about 1/3%.  That's more accurate than your LDR sensor.