Kusabi, Toriko 

A strange girl with long black hair who's usually accompanied by her friend Christina, a pink alligator.
She seems to have a connection with the mysterious man, Sundance.
Toriko is the female main character of the game, although you rarely get to play as her.
Unlike most female leads she is not a love interest nor is she some random girl who's magically special for some contrived reason.
In fact Toriko & Sumio don't really interact with each other. She acts more like a buffer between you & Sundance.
To top it off, Her & Sumio never meet each other through out the entire game.

She is the beautiful girl who constantly appears in Sumio's dreams ever since he arrived at
Hotel Flower Sun & Rain.
It's not certain, but some how she ended up lodging at the same hotel as Sumio.
She raises a pink pet alligator named “Christina”.
In Sumio's reoccurring dreams, Toriko is often depicted chasing after Christina.
(Who usually escapes from Toriko's hotel room.), Toriko is usually seen tracing the route where Sumio walked during the day time.
Judging from her speech and behavior it's plainly visible to see that she is alluding to an upcoming crisis that will befall Sumio Mondo.
It is not known whether or not the Toriko Kusabi who we see during Flower, Sun & Rain even exists.
Is she a figment of the imagination or is she the genuine article?
Sumio some times ponders if this woman form his dreams is a past sweet heart/girl friend or what not.

Toriko & Sundance were originally planned to appear in the "Silver Case". Both characters have concept art, but they were not actually used during the game.
Toriko Kusabi Silver Case concept art
Click thumbnail to enlarge
Toriko is the daughter of Tetsugoro Kusabi.
During the Silver Case, Tetsuguro Kusabi often broods about how his daughter
Toriko often despises him due to his excessive smoking habit.
You know what they say,like father like daughter.
Although Ms. Kusabi acts nothing like her hard boiled father at all.
(Tetsugoro Kusabi is one of the key characters  from Grasshopper Manufacture's debut game,"The Silver Case". He led a one man crusade against his former allies at the HMD & killed every single one of them. Well almost, Sakura Natsume shot Chizuru Hachisuka in the face. ")

Who is Toriko Kusabi  

  Toriko Kusabi, from what I gather is probably an astral projection like Kun Lan from Killer 7.
This explains a lot to me, since it pretty much explains why she has a pink talking alligator & why only Sundance can see & interact with her.

Peter Bochwinkur, a rather stocky man

who drove you to Hotel FSR during the beginning of the game.
He claimed to be looking for somebody & he heard that the person he was searching for was currently seen at Lospass resort.
By the end of the game he tells Sumio that he couldn't find who he was looking for.

After the credits roll & the last monologue with Peter & Sumio occur.
The FSR game all of sudden transforms it's graphic style to look & sound more like the Silver Case.
It's than revealed that Peter Bochwinkur was actually Sumio's partner from the Ward 24 Felonious 2nd division, Tetsugoro Kusabi from the Silver Case.
(Sumio saw him as Peter Bochwinkur because Sumio was still living inside a dream.)

Left: Toriko Right: Her father, Tetsugoro

Which means the person who Peter/Tetsu was looking for was his daughter Toriko Kusabi.
Unfortunately for him the Toriko Kusabi of Lospass Resort possibly never existed as she was only seen during Sumio Mondo's dreams.
(Sumio assumes that Toriko is just one of his many ex girlfriends from his past.)
The only other time she ever appears is when she & Sundance exchange dialogue.
Again this is probably metaphoric.
Sundance is most likely talking to himself since nobody else in the game including Sumio can see or hear Toriko Kusabi.