UChicago is not strong in theater. Stanford isn’t either, but it probably is a little bit stronger than UChicago. Neither is remotely close to places like Northwestern, NYU or CMU.
For political science and IR, UChicago is exceptional. In addition to a strong traditional faculty in these areas, David Axelrod’s non-partisan Institute on Politics brings dozens of speakers to campus, finds hundreds of internship opportunities all over the country for undergrads, conducts workshops, and brings several politicians to live on campus each term to teach students the practical realities of the business (this term these visiting fellows will include former Democratic governor Kathleen Sibelius and the 2016 campaign manager for Republican Presidential candidate Ted Cruz). The Institute basically jump starts students into careers in politics in a way that perhaps no other school can offer.
Stanford is very strong in political science and IR as well. The Hoover Institute is there (but it is mostly conservative and I believe it mostly has application to grad students).
Either school will serve you well.