Pittsburgh is a very odd and funky city. It's neighborhoods vary a lot, and each one has its own identity.
For architecture and neighborhoods:
Mexican War Streets on the north side are a must. Mid 1800s rowhome housing. It is a national historic area, and is a lot like Philly's old city.
Observatory hill is also a great place. It has the observatory, and awesome housing.
The south side flats are a must. Also carson street has all the shops, bars, and funky culture you will be looking for.
http://en.wikipedia.org/wiki/South_Side_Flats
Lawrenceville is another must. I just walked through that neighborhood last night. It has Pittsburgh style rowhomes going up a steep hill. I think it is a beautiful neighborhood.
http://en.wikipedia.org/wiki/Lawrenceville_(Pittsburgh)
Shadyside is a must: I refer to it as Pittsburgh's little San fran. Victorian homes densly filled into tree lined streets. Very yuppie, and just nice and clean.
http://en.wikipedia.org/wiki/Shadyside_(Pittsburgh)
A walk up the
Southside Slopes is great: these are above the southside flats. They go up a steep, very steep hill. The side walks are literally steps. You walk up the steps as you go up through this neighborhood. A good workout, and amazing views of downtown and the city.
http://en.wikipedia.org/wiki/Southsi...es_(Pittsburgh)
Oakland: This is where the universities are at. Lots of amazing architecture, compact, bussy, people galore. Pittsburgh's main library and muesums are there. It is Pennsylvania's "third downtown area." Another must see.
Squirrel Hill: My neighborhood. A very funky inclave of nice housing, old apartments, and one of the best neighborhood business districts in the city. This is where you will find awesome food, cool stores, and some cool neighborhood bars.
http://en.wikipedia.org/wiki/Squirrel_Hill
The strip District: another must see. This place was written about in National Geographic. Only Pittsburgh has a market like this. It is a open air, crowded, market place for food, and I mean good food. It is right outside of downtown near lawrenceville.
http://en.wikipedia.org/wiki/Strip_District_(Pittsburgh)
Give me time, and I will come back with more info on Jazz, stores, and other unique things besides the neighborhoods.
I would suggest searching the neighborhoods I have underlined in google. You will get maps to see how they are located in the city. For instance you can walk the strip district, and head down into Lawrenceville pretty easy. Pittsburgh is only 55 sq miles, so it isn't hard to bus around to these neighborhoods. I walked from Oakland to downtown one Saturday with no problem. But I walk a lot.