Two electrolytic filtering capacitors near or far away from each other?
should I place them near each other and near the power connector, or
place one of them near the power connector and the other one on the
oposite side of the PCB, for uniform voltage stabilization?

Place them where most needed with a view to minimizing circuit-current-loops carrying ripple current or noise current. The ripple/noise might be from the incoming supply or it might be caused by your circuit.
If both phenomena are present then you might wish to apply 100 nF capacitors local to chips or circuits that could generate high frequency noise/ripple and, place the electrolytics close to the incoming supply if there is significant ripple voltage that needs reducing.