I'd have to recommend The Other Josh Cohen in the Westside Theatre! It's a really charming show about an ordinary guy who runs into some less-than-ordinary circumstances, and it's overall just really uplifting. Also one of those musicals where the musicians are the actors, but they're absolutely fabulous in everything they do. It's $29 rush or $25 student rush (cash only, 1 per ID) day of, and when I rushed at the beginning of December I just showed up right at noon when the box office opened and there was no line.
Otherwise, something at New World Stages is always a good bet too. Jersey Boys has rush for $30 and Avenue Q has rush for $26.50 (which, if you haven't seen Avenue Q, it's the perfect college musical and might be particularly fun for an English major). If you're a Harry Potter fan, then Puffs is a fantastic play which also has student rush for $22 (1 per ID). All of these are cash only I believe.