I am a UW grad who lives in DC.
You are not going to go wrong with either school. The question is more, do you want to live in DC or in Madison.
Madison is the quintessential college town, with bigtime college sports and school spirit. As an IR major and out of state, you will be able to make the campus feel smaller through your major and classes. Keep in mind, a lot of those 30,000 students are Engineering or Ag - you pretty much won’t see them after your dorm in Freshman year.
Being at GWU in DC and having job/internship opportunities right there is also unique. It is a highly urban schools, located in the same neighborhood as the IMF, World Bank and State Department.
So to me, it is really about setting. I love DC but I wouldn’t trade my undergrad experience in Madison for anything.