Hello!
You might want to try one of the many restaurants on Mount Washington. There is a wonderful view of the city of Pittsburgh. My personal favorites on Mount Washington are the Georgetown Inn and the Shiloh (but the Shiloh does not have a good view of the city from inside the restaurant). Here is a link to an article about some of the restaurants on Mount Washington. Another unique thing about this area of Pittsburgh is that you can ride one of the inclines to get to the top of Mount Washington!
http://pittsburgh.about.com/od/rest...nts_Dining_Atop_Pittsburghs_Mt_Washington.htm
http://incline.pghfree.net/restaurants.htm
And at the bottom of Mount Washington is Station Square. Station Square is an old rail road station. It has been converted into a lot of shops and restaurants. It houses the largest restaurant in Pittsburgh, the Grand Concourse. It is an excellent place to go for Sunday brunch! Also at Station Square is a Melting Pot (which is not unique to Pittsburgh) and Pittsburgh's Hard Rock Cafe. Here is a link to Station Square:
http://www.stationsquare.com/main.asp
Someone else mentioned Max's Allegheny Tavern which is located on Pittsburgh's North Side. I agree, it is a great German Restaurant.
http://www.maxsalleghenytavern.com/
The Penn Brewery is another German Restaurant and they brew their own beers. It is also in North Side.
http://www.pennbrew.com/
The Church Brew Works is a different kind of restaurant. It is housed in an old church, and they brew their own beers there! I am not a beer drinker, but they say that their beers are excellent. It is located in the Bloomfield/Lawrenceville section of the 'Burgh. Here is their website:
http://www.churchbrew.com/
My all-time favorite is the Hyeholde Restaurant. It is in Moon Township, which is in the suburbs of the city. Their food is excellent, but pricey. The atmosphere is very nice. Just take a look at the photos from their website. It looks like an old castle.
http://www.hyeholde.com
And then there is the Primanti Brothers as mentioned above:
http://www.primantibrothers.com/
If you have any questions, just ask me. I grew up in Pittsburgh, and now live just outside of the city. I hope you have a great time visiting Pittsburgh!