Sections of the north shore are very nice and quiet. The Mexican War streets have some awesome homes. If you could get a place there I think you would really like it. There are a couple of traditional B&Bs in the area that can be very nice. It would not be an awful far walk from the light rail.
If you are looking for more action then south side might be in order but the light rial is not as easily accessible. Though there is a pretty decent bus service.
A lot of the tourist stuff is spread out in Pittsburgh so there’s no one perfect choice. Downtown is often the best and there are a good varieties of hotels. If I were doing an Airbnb, I’d look in the East End like Shadyside, Squirrel Hill or Oakland.
The North Shore hotels are handy too. The Northside is convenient to a lot but you need to be careful on exact location. Nothing will be awful but some won’t really be good.