Correct way to measure circuit power consumption before or after LDO
It really depends on what you want to measure. If you want to measure the circuit minus the LDO (which you presumably have some control over) then you can put it after the regulator. If the regulator draws significant current that can help separate the two.
If you want to measure the total draw (for example, to calculate the battery lifetime) then you would want to put it ahead of the regulator.
Since the current measurement will affect the voltage a bit, there may be some advantage in accuracy to  put it ahead of the regulator.
Since you have a linear regulator, to a first approximation the total current into the regulator will be the quiescent current of the regulator plus the output current. Some regulators have Iq in the  uA range so the two currents will be almost the same in many cases. Some regulators (particularly older bipolar types) may draw additional current that is related to the output current and possibly related to the proximity to drop-out. Usually that's not the case for CMOS regulators.