I loved Brussels. I haven't travelled too extensively in Europe but it's my fav city over Amsterdam, London.
I had to do it, I got suckered at a tourist trap selling Belgian Waffles drenched in Belgian Chocolate

oh it was good.
Beers are good too..
I took a bus tour.. hop on hop off deal.. was maybe EU15? It's worthwhile, me thinks for a day if you're on a limited time frame.. hits most of the major attractions.
I too am a poli sci student and saw the EU buildings.. but wasn't overly impressed... looked like a large business complex more than anything else. I didn't inquire about tours either.