If I needed to filter the power supply to the nano, I would use a ferrite bead instead of the resistor.
The thing about linear regulators, such as that in the Arduino Nano, is that they don't react fast enough (have a high enough bandwidth) at higher frequencies so they can't filter out high frequency noise from things that switch (like motor drivers). They react fast enough to slower changes (lower frequencies) appearing on their input so that the output remains constant, essentially filtering out the noise, but not high frequencies.
You normally want to get short out the noise (give it a low impedance path to ground) before it gets to the sensitive components with parallel capacitors if you can. Capacitors are more ideal than like inductors, ferrite beads (a specialized lossy inductor). They also have less loss than than series filtering components
But capacitors have a parasitic series inductance that will limit how well they pass really high frequencies which directly influences how well they appear as a short-circuit to GND to noise. It is usually at this point when you start throwing in ferrite beads. You tend not to want to throw in ferrite beads or inductors because they resonate with the capacitor (and other parasitics) and if they resonate at your more prominent noise frequencies, they will actually amplify that noise rather than supress it.