Usually in shard based games RP players tend to use either instance 3, 7, 10 or 69 as their shard of preference and as a way to meet other RPers. In Champions Online most of the RP takes place in shard 7 and 10 in club caprice...although the vast majority there seems to be less about character's stories and more about cybering.
In STO most RPers use fleets or stick to instance 7 when available. Most "mature/adult content oriented" RP takes place on Risa. (Or so I hear...cannot say for sure.) Most other RP takes place in the various space station bars/lounges, but isn't usually adult in nature.