We remember many memorable things about Beauty and the Beast: a rose, wolves, a singing teapot, and of course a beast. One of the things we may not remember is that though Belle is now living in a little home in her French village, she is the daughter of a rich merchant and once lived in a mansion. Unlike her sisters who desire expensive gifts when they can get them, Belle is moved by love, not riches riches (which is why she is unmoved, even repulsed, by Gaston's sexist and presumptuous behavior). This entire village setting, then, prepares her for accepting, and eventually loving someone based on things other than outward beauty or money.
Even though Belle is a prisoner in the Beast's castle, she soon feels comfortable there, though of course getting comfortable with the Beast takes longer. When she arrives, she is placed in the tower as a prisoner until the Beast comes to see her:
Beast: I'll show you to your room.
Belle: My room? But I thought...
Beast: Do you wanna stay in the tower?
Beast: Then follow me.
The tower is one place she is happy to leave and is thankful to the Beast for allowing her to have free reign (except for the west wing) of his home. To that extent, then, the tower is a place which ultimately makes Belle think more kindly about her captor.
She is taken to a lovely bedroom of her own, another lwonderful and unexpected surprise for the girl. This must surely make the Beast just a little less "beastly" in her eyes.
Another setting which helps to soften Belle's feelings toward the Beast is the library. Back in the village, Belle had always been considered rather an oddball because she loved to read; here, she gets to read everything she wishes as often as she wishes. The extensive library, as well as permission to use it, surely makes the Beast look better in her eyes.
The dining room is a source of conflict between Belle and the Beast, of course, but it is a setting which Belle comes to love because of the delightful (though rather odd) friends she makes there. Each of the servants who have been transformed into inanimate objects are kind to her, even putting on quite a famous show for her on the first night she agrees to come to the dining room. Feeling like she has friends in the castle both serves to soften the sense that she is a prisoner and casts a more positive light in the Beast. How can he be so bad if these are the people with whom he has surrounded himself?
The forbidden and gloomy west wing does not seem to be the kind of place which would help Belle feel more kindly toward the Beast; however, the demonstrations of violence she both sees (slashed portrait) and experiences (his terrible display of temper when he discovers her there) reveal to her how unhappy he is. He is not just a beast in appearance but is suffering from his condition as a beast.
The transformation in Belle's feelings for the Beast are revealed in another significant setting in the story. The balcony is the place where the Beast finally decides to fight for his life against the enraged Gaston, and it is the place where he nearly loses his life. Most importantly, Belle looks into his eyes in this moment of near-devastation and loss and discovers that her feelings toward the Beast have changed from friendship to love.
The final memorable setting in the story is the ballroom, the place where the love between Belle and her "beast" is fully revealed to everyone. This room does not change Belle's feelings, but it does reveal them.