Though there are several good hotels, downtown, I enjoyed staying in East Liberty. Here I could easily get to the nearby neighborhoods to visit museums or popular restaurants. My recommendations include:
Hotel Indigo Pittsburgh East Liberty: This is a contemporary boutique hotel with 135 rooms located in East Liberty. It is in walking distance to a number of restaurants, cafes and shops and a short drive to museums, restaurants and other neighborhoods. 123 N. Highland Ave.
Inn on Negley: Located in Shadyside, the Inn on Negley is a Victorian mansion that has been converted to a luxury B&B with eight lovely guest rooms. They are open to the public for dining and offer breakfast and brunch as well as a traditional afternoon tea Wednesday through Sunday. 703 S. Negley.
If you want to stay downtown then the historic William Penn Hotel is a good option. Totally restored it is an Historic Hotel of America. 530 William Penn Plaza.