How to model the motor for this PWM motor driver circuit and is this simulation reliable?
For the inductance I cannot think of any other simpler way than measuring it with the help of a signal generator and an oscilloscope as described in this similar question. A more comprehensive DC motor simulation walk-through can be found at this website. 
First thing, since the supply voltage can reach 24V, you should limit the maximum \$V_{GS}\$ of the MOSFET to below 20V via a zener diode. 
Add small capacitor close to the motor, in order to reduce the line impedance during start-up. You might also want to add a small series resistor to the MOSFET's gate in order to limit current peaks. 
From your simulation, there is some ringing during the off-phase of the MOSFET. This comes probably from the resonance of the motor's inductance with the output capacitance of the MOSFET. You can reduce it by adding a snubber (in this case a small cap in parallel to the drain-source ends of the MOSFET, therefore reducing the ringing frequency).