Heading directly north from the entrance will take you on the path to the throne room and the boss above. A bit of exploring nets you some cash. The eastern path contains 3,000 gil in two chests. The stairs and room you'll see further west are inaccessible for now. The northern passage on the east side leads to a chest with 1,000 gil, while the southern path leads upstairs to the third floor.
When heading to the secret basement, there is a gap in the east wall that leads outside the castle, and another gap to the south leading back into the castle where you will find a Treasure room.