The following two movies are uneven, but I still liked them for various reasons, including the fact that they're sometimes ridiculous. They're both theater stories, specifically stories of women trying to make it big in musical shows. Neither of them has amazing dance scenes.
(A movie I highly recommend, better than either of these and more witty, is Stage Door, which I wrote about here. It's also a much better choice if you want a non-musical drama and comedy; there are some brief scenes of dancing, but no musical numbers.)
Title: Dancing Lady
Director: Robert Z. Leonard
Rating: Not rated
Dancing Lady is watchable mainly because of Joan Crawford in the lead as Janie Barlow, who wants to move up in the theater world from burlesque stripper to Broadway star. Crawford had some dance training in real life, but her chief strength is her acting, and she gives this movie some depth by showing just how much her character lives for dancing. It's a slight movie, not too long, the first half snappy and well-paced before too many clichés pile up.
She has to pick between two men, one of them played by Clark Gable. I've yet to see a Clark Gable character I like (I haven't watched Gone with the Wind, but I doubt it will change my mind about him). I don't like what I've seen of Gable's acting style, which usually consists of him growling at people, including the women he's supposed to be in love with. In this movie he isn't terrible, largely because he and Crawford have good chemistry.
The movie is also notable for being Fred Astaire's first film role, where he plays himself, and Gable addresses him as "Freddy." The only thing I remember about his dancing in this film is that he wears lederhosen during a musical number with lyrics that rhyme "Bavaria" with "take good care o' ya." The big musical theater production at the end is kind of amazing as it could never take place on a Broadway stage (unless the stage were the size of a football stadium and the actors could change costumes in two seconds).
By the way, the Three Stooges also appear in this film. I don't know why. But somehow, with all these different bits of it hanging together, I liked Dancing Lady.
Title: Dance, Girl, Dance
Director: Dorothy Arzner (and, according to IMDB, also an uncredited Roy Del Ruth)
This movie centers largely on the rivalry that could maybe turn into friendship between two dancers: Judy (Maureen O'Hara) and Bubbles (Lucille Ball). One of them is a serious ballerina, lacking in confidence, who struggles to get a job but is dedicated to the integrity of her craft. The other, brash and cynical, sells her sex appeal to become successful in burlesque theater. (Based on their names, guess which one is which.)
A few things make this movie stand out. One is that the rivalry between the main characters has layers to it, and there's a sense that they shouldn't have to be rivals. Another memorable aspect of the movie is its look at how female performers respond to the gaze and expectations of the men in their audience. The movie sometimes turns its focus sharply on those men.
For instance, there's an audition scene where Bubbles puts on a hula dance for a prospective employer. The most shocking part of that scene isn't the risqué dance, but what the camera shows when it focuses on the employer's face. He emerges from the scene far more exposed, sexually, than Lucille Ball in her hula costume.
There's also another powerful moment when Judy responds to a burlesque audience that's been laughing at her. At some point in the movie, she lowers her expectations and signs on at the same theater where Bubbles is a star. Judy's job is to try to dance ballet seriously while embarrassing things happen to her on stage. The audience, largely male, depends on her humiliation for their gratification. It gets to be too much. She marches to the front of the stage, stares them into silence, and calls out the men and their ridiculous displays of what they think is sexual dominance.
The business has made Judy and Bubbles rivals for the attention of such an audience; that's the degradation they need to confront.