PCB design for current shunt monitor
The standard rule of thumb when amplifying sensors is to put the op amp as close to possible to the sensor, because the op amp has a lower output impedance than the sensor and so a given noise power will produce less noise voltage.

With a shunt resistor, though, the output impedance of the shunt is likely lower than than that of the op amp. This would argue for the long trace being between the shunt and op amp. However, the signal amplitude from the shunt is also much smaller, or else you wouldn't need an amplifier. Since any noise on the amplifier input will be multiplied by the gain, the tradeoff becomes a matter of comparing the impedance ratio with the gain.

All the typical advice about reducing noise still applies, of course, and will likely matter more than the amplifier placement: low-pass filtering, shielding, attention to grounding and current loops, etc. Your noise is going mostly to depend on the bandwidth you need for the current measurement.