All credit given to CyricZ on their great Yakuza Kiwami Guide on GameFaqs.
Yui is the hostess at Jewel. She's a bit reserved, largely due to the fact that she doesn't want customers falling in love with her. It'll be up to Kiryu to open her up a little bit more to conversing as a hostess.
Rank Topics
F Rank - I was in prison. -> At least you're honest.
E Rank - Men need to consider a girl's feelings. -> Honesty is the best policy.
D Rank - They're jerks. -> How about "I love you"?
C Rank - What a weird guy... -> Either
B Rank - That's certainly possible. -> Bet you're in love already.
A Rank - You won't fall in love, right? -> Looking forward to it.
General Topics
Taking classes - Cooking class
Plastic surgery - It's your sister's choice.
Class reunions - Maybe they don't like fun.
Buying presents - That's an old trick.
Toy poodle - The sooner you get him, the better.
Online reviews - You're not cute.
Picture taken - Just don't even smile.
Eighteen years old - Do you do that too? ->Challenge accepted.
Emotional movie - Age really matters.
Running late - I'm sorry to hear that.
Events
D Rank - Head east on Shichifuku St., near Kanrai.
B Rank - Go to Theater Square.
S Rank - Meet her in Theater Square.