How to filter the power supply for an Arduino in a vehicle (car, motorcycle)?
The solution depend on what causes the reset.

It might be EMI interference on the RESET, in this case a stronger pull-up might help. The standard pull-up for nano is 1kohm which should be enough but if you use a clone the value might be higher. 

If the reset comes from power drops then only a higher capacitor on the regulator input would not be enough since you also have other consumers on the 12V line that will suck the energy stored in the input capacitor. 

Feed the capacitor and the regulator input through a diode, anode to 12v, cathode to capacitor/regulator. This will stop the energy stored in the capacitor to go back to the 12V line.