Since the play's setting, a small Kansas town in the 1950s, is essential in the development of the characters and conflicts, consider it as a possible subject for study. Does the setting affect the characters' behavior and/or determine their lives? If so, how? Since a strong argument can be made that it does, one thesis might be to state the idea: The setting of the drama acts as a deterministic force upon the lives of the characters.
This thesis would lead you into a discussion of the social structure and social mores of the 1950s in the Midwest, especially in relation to the role of women. Since the major female characters represent three distinct age groups, they show the influence of the setting upon women at different stages of their lives.
Another interesting element to research in the play is the theme of loneliness. An easily supported thesis would be that Inge's major characters in the play are studies in loneliness and isolation, leading lives without fulfillment while they long for something more.
In terms of secondary sources, finding them to support either of these thesis ideas should not be a problem. Picnic was a popular and celebrated drama when it appeared on Broadway, and it generated a great deal of literary criticism, analysis, and discussion. Good luck with your paper!