I've lived in the Pittsburgh area for 26 years and have lived in the city and north/east/south and west of city.
If you want a good house in that price range and don't mind a 30 minute commute each way, the North Hills are the only option. Any other suburb will be mired in traffic at rush hour but Route 279 north and adjacent trunk roads provide a predictable ride.
I commute into Oakland near Pitt from the North Park area(a running mecca) and am usually in the office within 30 minutes.
Shadyside, Squirrel Hill, Regent Square and Point Breeze are in the city and all have some beautiful neighborhoods but some of those beautiful neighborhoods are within blocks if not feet of dangerous streets and a house that goes for 250k in the North Hills could be twice or even four times as much in those nicer city neighborhoods.
The Pittsburgh city schools are horrific and violence is common even in the nicer areas and you will pay extra income taxes inside the city limits. Being near Oakland and downtown will, however, keep you handy to a wide menu of cultural and sports attractions.
Commuting to the city from the east, south or west could cause you to shoot yourself esp. from the east(Monroeville Murrysville, and Plum).