The Carnegie LIbrary in Mt. Washington is right on Grandview Ave. It's a great location - you can walk outside the doors and see the entire downtown area below! The library itself has a small selection which is better geared towards children than adults. Although, they do have a limited selection of books for adults. They also have computers that you can reserve time on when you get there.
One thing that they are known for is their great summer reading program that encourages children to read, read, read! They give them stickers and enter the kids into raffles for prizes when they read over the summer.