6 weeks with 12 and 13 year old sons

we land in Rome on Jan 19th and Leave out of Milan on Feb 28

January 2017, as in just a few weeks from now?

yes, like I said, we are 'spur of the moment' travelers, I have my eye on some airBnB places in Rome for the first week. and then thinking Sorrento or Pompeii after that, but not sure where we will head next...

If you will only be using public transportation, and in the winter, small towns may not work very well for your trip.
But I think you will find that you can feel like you're in a small town in some of the neighborhoods of Rome, Florence and Venice.
In Rome, we once stayed in Trastevere, which felt more small-town, but then it was farther to get to many of the sights in Rome.
In Venice, I really like the sestiere of Cannaregio. Carnival in 2017 is February 11-28, so I'm guessing the city will be packed then, and prices will be high. Also, that's the time of year when the city might experience "aqua alta;" google that term for details.

In the area roughly between Florence and Venice there are many, many attractive historic towns and cities. Bologna is a rail hub that's a good base for visiting many of them. It's a large business-oriented city (not a cute little town), but it has a large historic district many of whose streets are arcaded, thus providing good protection from inclement weather. From Bologna you could visit Ravenna (smallish city with a lovely historic district and many churches with fabulous mosaics), Ferrara, Modena, Parma, Padua, Verona and (more of a stretch) Vicenza. I enjoyed staying in Padua and making my trip to Vicenza from there. Padua, Vicenza and Verona are also within easy daytrip reach of Venice, but hotels tend to be costlier in Venice, so I've been reluctant to use that city as a base for daytrips.

Day 20-27 Arrive Rome taxi to Roma termini, train directly to Naples. Then Circumvesuvian to Sorrento, or Naples or split your time between the two.
Look at the Campania arte card. Lots of sites in both areas.

Day 28-03. Rome.

Day 04-07. Orvieto.

Day 08-15. Florence.

Day 16-20. Venice.

Day. 21-24. Bologna.

Day. 25-28. Milan.

There are great day trips from each city and you have plenty of time.

This trip is very doable with a budget. We like to stay in apartments, it allows us to fix our own breakfasts, for lunch we grab a pizza or sandwich from one of the many small grocery stores around.

In Venice, do not be afraid of aqua alta. I took my soon to be wife there and we enjoyed the trip. Just ask or look up when it is expected to occur and then head to higher ground. The tourist office can help show you where those places will be. We entered St. Marks and when we came out, about a quarter of the walkway between the church and the canal was flooded. We would actually stop and watch the water creep across the stones. For us, it occurred mid morning, so we went to the lowest places first and then ventured to higher ground as it peaked. The city sets up raised platforms to walk through the lowest areas, which helps. Some travelers had waterproof boots, $20 from places like Tractor Supply, or bought locally. We were just wearing our normal hiking boots.

If you can nail down your itinerary, you can purchase train tickets that are super cheap but not changeable and non refundable. They are on sale now.

This is not the most ideal time to travel in Italy, as many museums and other attractions will be operating on reduced hours, and the weather may not be the best. As you're from Alaska, I'm sure you'll be able to deal with the weather.

I'd highly recommend packing along a copy of the RS Italy guidebook, as that provides an enormous amount of information that will help plan sightseeing, accommodations and activities. I doubt that you'll find much cycling or horseback riding at this time of year.

If you haven't travelled at all in Europe, I'd also recommend reading Europe Through The Back Door prior to your trip, as that provides a lot of good information on how to travel well in Europe.

If you haven't travelled in italy before, there are some potentially expensive "caveats" to be aware of when using trains and other public transit. If you need more information, post another note here and I'll provide further details.

The lowest cost accommodation is usually Hostels, and some have private rooms which may work for a group of three.

Well, since you're budget travelers, I think you'd better scrub staying in Venice, especially since your route will land you there at the very end of Carnevale. What you can do is stay in Padua or farther Verona, where you might get reasonable room prices and then day trip by train to Venice once or twice to see Carnevale which is an unforgettably experience. I like Verona more than Padua, but it will be easier to get to Venice from Padua. Or go to Venice early on then with some backtracking.

Trains are easy to use. Fast trains are expensive but with a 6-week stay, you may want to opt for the less comfortable and much slower regional trains.

Think about spending a few days in Salerno instead of Sorrento. It will probably be cheaper, both for a room and for food. You can day trip to Paestum (ancient Greek temples) as well as Pompeii and Sorrento.

I wonder if small towns is even possible in mid-winter. In off-season, even if you find a room there may be nothing to do after dark (around 5.30-6.00) but stay in. At least in the cities, there will be things to see and do.

RE: "...if something 'good' comes up, we will take it." You have plenty of time to do side trips. In Rome go out to Ostia Antica -- only takes 3/4 of day and is close and cheap on public transit. If you go to Pompeii, you might as well toss in Herculaneum as well as they are not that far apart. Do one in the morning and the other in the afternoon. In Venice, don't overlook a day trip to Murano and Burano. Verona is also close by and can be done as a day trip, but two full days might be better depending on your interest in the history there.

Since you are going to the Pompeii area, why not go down the coast to Maratea, a beautiful, small town in Basilicata and right on the beach. You might also want to go to Sicily, which is certainly warmer than northern Italy and has many Greek ruins. All of the cities there are interesting and the town of Taormina is hard to beat for beauty, with a fantastic Greek theater. Wherever you go, you will have a memorable trip.