The three of them decided to split in order to cover more ground. It would be ineffective if they were to just move in a group with such a large kingdom. Lycan covered the noble area as he is still considered a noble despite the empire being dispersed due to war.
Solstice covered the middle area where the merchants are placed as her family have many connections to merchants. It seems that the vampires managed to hide well by having multiple connections with merchants and their great information network. They became able to blend in society using this tactic.
Adrian is exploring the commoner area as he is basically just an adventurer passing by. He did not say anything about the commoner area despite it being the most difficult to gather information. He stayed quiet because spirits of the deceased are freely roaming this area and all he needed to do is do their requests to get information.