As others have said, if you are taking a job in Pittsburgh, you might be better off finding a decent neighborhood in Pittsburgh or in some suburb or town near Pittsburgh – other than Steubenville. You would still be reasonably close to Steubenville if you wanted to send your kids to college there eventually, without having to worry about them being too far from home. Maybe you would even be close enough to take a few classes there yourself. (But I don’t know; it sounds like the commute might be a bit much.)
Now if you are just looking for any good city to live in (from a Catholic perspective), and if you do want a bigger city rather than a smaller city or town, I would recommend that you consider St. Louis. I have heard good things about the Catholic community there, and I know that they have a beautiful cathedral and a recent history of very good bishops. St. Louis also has lots of good activities for families with kids. We enjoy the City Museum, the Magic House, and the zoo. The City Museum particulary is a must-see. I have also heard good things about the science center, Grant’s Farm, and a few other attractions. And of course, if you like baseball, the Cardinals are great.
Nashville is also a place you might consider. The percentage of Catholics there is small, but Nashville has some good parishes, a small but good Catholic homeschooling community, and several good Catholic schools thanks especially to the Nashville Dominican sisters. And they have Aquinas College, which is a small but orthodox Catholic college, also run by the Dominican sisters. Nashville also has good live music (and not just country), and it has a decent economy and a reasonably-priced housing market for a big city.