We are definitely open to checking out any neighborhood, as long as it is reasonably safe and has as many wish list items as possible: walkability, easy access to transit, close to one of our workplaces, parks/recreation, cool people, and solid K-12 schools. We both were raised in a "unsafe" city (my childhood home was randomly shot at on more than one occasion), so we know how to handle ourselves and know what to look out for.
We'd be pretty hesitant to buy until we have a better feel for the city and a bigger savings cushion. We have enough saved for 20% down in our target price range, a 2K emergency fund, but little else. Ideally, we'd like another year or two to build up more savings - enough for 1 year of mortgage payments, property tax, and bare bones living expenses, as well as a house maintenance fund. Then we'll be super-comfortable taking the leap into home ownership.
There's also no rush - our LO is 1yo so we have plenty of time to find the right place for us. That said, if anyone knows of a good rental house/duplex/townhouse near Mt. Lebo, Bethel Park, or USC - PM me :)