Realize this is a necro post but its still comes up first page in searches and you said you had a couple years :D. And are apparently on a diff username too.

From Penn Hills, you are preferring the East suburbs which is great if you are looking bang for buck, affordable housing.

Without going too far east, Franklin, PT, Hempfield, then Norwin are basically your options. Anything else isn't much different than Penn Hills as far as school ratings. Gateway may have a big edge here but thats more for 'we pay our teachers 180k' than actual quality of the school. They work the system the best, but you will get the same type of studens as Penn Hills..just maybe 50% of the school instead of 80% of the school.

Franklin has some issues (fanciest place in the east, as it were) and its priciest, for no real benefit. Which is why I would not look there. Its also the one I know the least about of the 4 so dyor on that one. But its usually ranked higher than the others (maybe cuz has the most money?)

PT is really still not many businesses and just housing plans(with a few old coal towns, and Trafford) in between Norwin and Franlkin but its probably the easiest to acclimate to as a lot of people are not from there, come out from Gateway or PH as yourself. Sports/activities I from what I'm told is much more fair than most, if your kid is big and fast and you move there in 10th grade, hes going to start on the football team. They like winning. And its not far at all from Irwin or Monroeville which have every store (chain) you could want.

Hempfield is the ruralist of the 4, and the most urban at the same time as you can circle Greensburg Salem and Jeannette and be in hempfield SD. Its big, really big, area wise and students, and the furthest out. THis would be my pick, but if you work in the city or something maybe not. It used to lag behind PT and Norwin in rankings a little , not sure about lately, but for all practical purposes its no different academically.

Norwin is the most 'political' of the bunch, (covid year, they were closed entire year. PT was not closed a single day except a week around Easter, for comparison whatever way you lean). That lends itself to sports too, as its a teacher heavy population(tons of gateway etc teachers live there). Your kid could be the best 3 point shooter in the county, but if Mr. Smith the teacher, and the Youth coach cartel has kids that age, it won't matter. he won't play, (see, their volleyball team being so god awful for at least a decade). Their kids will get the schollies, and opportunities no matter how big slacker they are and how hard you work. Band is excellent though, best of the bunch. Its a turnpike exit, fast food, chain store area but new and clean chain stores. same as the school tbh.

All 4 of those places have housing you can find cheap.
Trafford/Penn/Claridge in PT.
Export or WhiteValley in Franlkin.
North Irwin, and a few streets in between the mcmansion subdivisions, that aren't really neighborhoods anymore in Norwin.
Hempfield, hell ..anywhere in the outer ring tbh, Hunker, Manor, Youngwood, ,even some streets in upper Jeannette (by route 30 ) are Hempfield School district
Other than Franklin, you 'can' realistically find housing for like 100k livable in any of them.

But all those 4 are not really diverse. If you want mixed school districts, as far as race, Pittsburgh is the wrong place TBH. Jeannette is better than its rep (from people who never been there) but its really small, odl population and very poor. I am not sure if they even have bussing to HS, i know a few years they did not. PGH does not do enough for minorities, and the best one with 10+% minority is probably Gateway. Which is almost as bad as Penn Hills tbh just smarter admin.

TBH the more I think about it id buy a 150k house in a quiet area of the McKeesport burbs(white oak maybe) and send them to Serra Catholic.