Perhaps they would talk about Klaus's redemption arc in the fanfiction. If there is one, Caroline could discuss with Hope how Klaus was changing or trying to atone for his past sins. This would be an important conversation for Hope as she would want to know if her father was capable of change.
They could be talking about Klaus's enemies. Caroline has seen Klaus deal with many foes, and she could share those stories with Hope. This would give Hope a better understanding of the dangerous world her father was a part of and how he managed to survive all the threats against him.
One topic could be Klaus's art. Since Klaus was into art, Caroline could tell Hope about the side of her father that was an artist. Hope would be interested in knowing this aspect of Klaus as it shows a different side of him other than being a powerful vampire.