Pittsburgh is filled with all sorts of fantastic things to see and do.
Museums (for almost any interest. In adition to ehBeth's listing, there's the Mattress Factory and the Heinz History Center and the Mexican War street district.
Sports- it's baseball season and the PNC park, home of the Pirates is a short walk over the 6th Street bridge from downtown. Even if there isn't a game you can look in and see the field, get a feel of how magnificent it must be to be there on game day.
The Aviary (short walk over the bridge on the north side)
If the 2 of you are into walking, a walk along E.Carson on the south side is enjoyable, plenty of shops and places to grab a bite and see some older structures,
Be sure to head over to South Side. Right across the Smithfield Bridge you can grab the Monongahela incline, take a short ride up to Mount Washington and get a spectacular view of the city. Look towards your left while up there and you can spot Heinz Field where the Steelers play when at home.
Plenty of cultural events involving music as well.
Places to stay? I have tended to go big with the Omni William Penn. Have always lucked out with good room price by going through one of those online thingies.
Plenty of public transit...mainly bus, there is also a light rail system although it is quite limited. The T is free in North side and downtown. Buy a transit card on Smithfield (not sure of the exact address)