On one level, Nora's desire to be a dancer on Broadway could be symbolic of her overwhelming need to escape from her boring, unfulfilling home life. At home, she's nobody; on Broadway she could be a very important person indeed. Since her dad passed away, Nora's become increasingly dissatisfied with her domestic situation. She is resentful of her dad for dying and leaving her with a weak mother. She's also upset that her younger sister, who suffers from a heart condition, gets more attention than her.
Making it as a dancer would give Nora the opportunity to break free from her present condition and become somebody in life. It would give her the chance to be the center of attention. To some extent, Broadway would also give Nora a new home, something to which she attaches such great importance. Nora is tired of being a boarder in an over-crowded house and desperately wants a place of her own. Although being a dancer on Broadway wouldn't necessarily help her achieve that goal, it would at least give her a place in life. A place is something she palpably lacks at present.
As with many people who go into show-business, Nora is somewhat emotionally needy. Rightly or wrongly, she doesn't believe that her mother loves her Becoming a star on Broadway, with all the popularity that entails, is one way of finding a substitute for the maternal love which Nora believes herself to be starved.
In summation, then, one could say that Broadway represents all the things that Nora wants in life but doesn't currently have.