There is no airport to target or avoid, per se.
Malpensa (MXP) gets nonstop flights from the US, but not from Philadelphia (closest airport with MXP flights is Newark). In addition to good links to Milan, MXP has direct coaches to Turin and Genoa. And there are two train lines from the airport to the city; one is to Milano Centrale, which has trains to the whole country (and Switzerland).
Venice (VCE) gets nonstop flights from Philadelphia for part of the year. VCE is not only good for Venice, but it has a bus to Venice Mestre station, with trains to the whole country, so it's good for anything in the area (for instance, a friend of mine got a train to Udine).
Rome (FCO) gets nonstop flights from Philadelphia year round. It is of course in central rather than northern Italy, but it has trains to Roma Termini and Roma Tiburtina stations, which again will have trains to lots of places. In particular, it's only 90 minutes from Termini or Tiburtina to Florence, so Rome can be a good option for this.
Other Italian airports will require a change somewhere. If you want to fly closer to your destination, rather than flying and taking a train to it, some northern Italian airports are Genoa, Turin, Milan Linate, Bergamo, Verona, Trieste - and I'm probably missing a few. Many of these have flights from Munich or Frankfurt, which in turn have service from Philadelphia.
If taking a train from 30th Street Station to Newark airport to get a flight to Milan or Rome is an option, you used to be able to get this all on one ticket, by going to Continental's website and using the "airport code" ZFW ZFV. This code did not always work on other websites. Now that Continental has been absorbed by United, I don't know if this still works, but you can try it. Again, Newark has nonstops to Milan Malpensa, so this "train to the plane" can be an easy way to start a trip, particularly if you are going outside of the months of the nonstop from PHL to VCE.
To learn who flies where from an airport, look at that airport's Wikipedia page, under "Airlines and Destinations." And to see how you might get from an arrival airport to a less obvious destination (say, Malpensa to Bologna, or Venice to Ferrara), a great start is Rome2Rio: https://www.rome2rio.com/. Note that it is only a start; you should always double check with the bus company, train line, etc.