Traces from shunt to amplifier must be routed as a differential pair to reject interference.
Now, your current sense amplifier has a "REF" input pin, to which the output is referenced. Wether you choose to place your INA close to the micro, or close to the sensor, keep in mind this: if REF is connected to GND at the INA, then any noise in GND between this point and the ADC's GND will be added to the measurement.
REF should be connected to the ADC's GND pin (in this case, the microcontroller).
This means you can also route these 2 signals (INA output and REF) as a differential pair, because this is what they are. They carry a voltage difference.
Now, where to place the INA? This is hard to say without seeing your board. If you stick it right next to the shunt, but then it sits next to a DC-DC and you power from a nearby dirty rail... maybe a bad idea. But tiny voltages on long traces in a noisy environment isn't that good either.
I'd place it as reasonably close to the shunt as possible, but I'd be wary of GND noise. Some filtering on the inputs can't hurt, but beware where you connect anything labeled GND, like the bottom end of those filter/decoupling caps and of course the INA's GND... make sure it doesn't sit on a minefield of DC-DC ground noise. Like, in the current path between the DC-DC input and output caps and low-side MOSFET...
And a ferrite bead + cap in the supply could help, too.
Remember your nice INA might have 100dB CMRR at DC... but it has 0dB CMRR/PSRR at 1MHz.
If your signal is slow and polluted with HF spikes, a simple RC filter at the ADC input can also work wonders.