Using shielded audio cable for potentiometer sensor
Why don't you connect potentiometer as people normally do, between GND and VCC? If you use 5-10K potentiometer you'll see much less noise on the input.

The reason you see so much noise is that your source impedance is too high, you simply don't allow enough current through to charge sampling capacitor in ADC. You cannot use less then 22k if you use internal pull-up, while ADC in MCUs usually optimized for about 10k source impedance.

There are three methods we use on electrical scooters with about the same distance to multiple resistive sensors.


add 0.1 uF capacitor between the wiper wire and GND right before MCU pin. The capacitor performs two functions. First, it filters out high frequency noise. Second, it further reduces source impedance by acting as local low-impedance source during sampling.
use shielded cable with shield connected to system ground near MCU. In your case this is not an option, but you might see some noise reduction if you connect shield to GND.
add ferrite core to high current switching power lines. Again, this might not be the case for you.


In short:

1) use 5-10K potentiometer
2) connect it between VCC and GND
3) disable internal pull-up
4) add 0.1 uF capacitor near ADC pin