I don't know where there is a definitive list that includes plots. However, i glanced at Wikipedia, and they do list all the episodes, and many if not most of these have their own link which leads to an episode page, many of which have plot synopsis.
http://en.wikipedia.org/wiki/The_Twilight_Zone_%281959_TV_series%29#Season_1_.281959-1960.29

Hope you find it there. Let us know.