As someone who may very well turn down some big name schools for a better-fit school and program with less general name recognition, I have to say that fit is very important. You're going to be at the school you pick for 5-6 years. When you're happy and feel supported (not necessarily even financially, mind you), you are likely to do better work. The quality and originality of the work you do, in my opinion, matters more than the name.
Furthermore, you have to differentiate between how political scientists will perceive the name and how the general public will perceive the name. We are mostly on an academic track, so our school's standing among our peer group - particularly people within our SUBFIELD that will ultimately be evaluating our work - matters more than how our friends and family will react.
My two cents.