I generally tend to fill all remaining space with copper polygon on both sides. Then i join both sides with randomly placed vias (have to be randomly placed to avoid accidental resonant circuits). If there are some areas in a polygon which i cannot connect to proper potential or some large "antennas" i tend to remove those. If your designing a mixed signal circuit, then laying out ground and power is much more complicated, but if you're designing such circuits you probably know that stuff