The Glass Menagerie is a largely autobiographical piece. Williams' own sister, Rose, was declared mentally unstable and underwent a lobotomy. This is something Williams felt guilty about in his own life.You might consider analyzing the autobiographical nature of Laura to Williams' sister as well as the connections between her character in this piece and the similar character in both Rose Ta too and the short story Portrait of a Girl in Glass.
Like Tom, Williams was a gay man struggling to be a writer and to live in a world where homosexuality was frowned upon. This is a second autobiographical theme that you might want to examine.
Moving away from the directly autobiographical elements of the play, there is also a conflict between the past and the present - the world of the movies and modern life that exists outside of the fire escape and the world on the inside where Amanda struggles to hold on to a past, a Southern gentility that no longer exists. She refuses to engage in the present for, if she does, she will have to admit that she has lost her youth.
Fragility is another theme. Laura is fragile like the glass that she plays with. In what way does Laura reflect her own fears and desires through her glass. She is "broken" (her limp) and her unicorn becomes broken. There is a parallel between the uniqueness and of the unicorn, which becomes "normal" and Laura's own uniqueness.
Those are a few ideas to get you started!