If your into architecture like me, you should really make the Cathedral of Learning Tower a destination. Not only is this one of the finest, and tallest Gothic buildings in the U.S., but each of it's classrooms display a different architectural style from around the World.
What impressed me the most was the magnificent multi level space on the first floor that not only had beautiful vaulted ceilings but they were made of stone. Since I've studied Architecture, and it is my topic I can tell you that this appears to be an extremely authentic Gothic interior and is very identical to the grand Cathedrals in Europe. Another cool thing about the Cathedral of Learning, is that it is located in one of the most gorgeous places I've seen anywhere. You can get a real nice view of the area from the 36th floor of the Tower (see my photos).
From here you can see many of the gorgeous mountains that the city is sculpted into as well as some of the neat buildings and neighborhoods in the area. There is also an outdoor observation deck but unfortuantely that is usually not open to the public, can't figure out why. On my first visit here I lucked out because the Tower was being restored so I was able to sneak out on it, man was that something. Don't bypass Pittsburgh it's an amazing City.