Sentou no Musume!?

The story

After Mizusawa Yume's mother becomes ill and passes away, she finds a picture of a man holding a baby in her mother's keepsake box. On the back of the picture it says "Loving Papa and Yume, at Raku no Yu." Yume has never known or even seen a picture of her father, but she believes that this guy must be him. Also in the box there is a lighter with the initials RM. After she finds that the "Raku no Yu", is a 'sento' (public bath) in Shibuya, Tokyo, she's off to meet her long lost father and to get as much money out of him as possible. The debts her mother left her after her death left nothing for Yume. Yume blames her father for her mother's death because if it wasn't for him she wouldn't have had to work so hard and wouldn't have gotten ill and died young. Once she arrives in Tokyo and finds 'Raku no Yu' she finds a name plaque with the inscription Mannaka Rokku, so she is sure this is the place.