You are in the Pittsburgh Public Schools. Taylor Allderdice is the top ranked public school in the city. http://www.pps.k12.pa.us/allderdice/site/default.asp
It is located at 2409 Shady Avenue, Pittsburgh, PA 15217 (Squirrel Hill).
Since, you are not in the feeder pattern for Allderdice, your student will have to study Manderin Chinese or enroll in the Engineering Magnet program in order to attend. If you have a child who is gifted in the Arts, the Creative and Performing Arts High School in Downtown Pittsburgh is another good choice.
If your child is male, there is Central Catholic High School that is nearby to you. My experience has been that males that graduate from there tend to be too chauvinistic for my liking.
Allderdice has been consistently ranked a top school and would be my first pick school. I would choose it over the local private schools. Good luck to you.