what's the most entertaining way to go from San Francisco (SFO) to Milan area?

I fly to Italy from SFO once or twice a year. Always non stop from SFO to Europe first via the Arctic route (going through NYC or anywhere in the East will significantly prolong the trip and will be subject to delays in the congested and thunderstorm prone Eastern US). Next week I'll fly to Italy from SFO via CPH with SAS.
The most entertaining way to get there is the fastest way possible at the best price. That should be your guiding principle as well, especially since you are traveling with small kids. I read somewhere that you are moving to Varese to study. You will therefore have plenty of opportunities to take the trains around during your stay. Why prolong the agony of a very long journey when you and your kids will be jet lagged?
At most I would consider a stop of a couple of days in the EU hub where you must have a layover (there are no non stop from SFO to MXP). Some airlines let you to prolong the lay over to a few days (instead of just a few hours) at no or no significant extra cost. Of all EU cities with non stop link to SFO, Paris, Amsterdam, London and Copenhagen are my favorite. However not sure if a 5 and a 1 year old would care much about any of them.

Since Varese is your destination, why not just fly to Malpensa which is just a cab ride away? Delta/Alitalia has a good connection through JFK. I know it is not as scenic/romantic as other routes, but it is liable to be the least amount of pain with two small children in tow. Zurich is the closest as far as nonstops go, and Swiss International does a good job.
Edit- I would also add that since are staying long term and travelling with small children, you will be traveling "heavy". Not just personal gear, but with all the accoutrements for taking care of the kids, strollers, etc. That makes changing trains a bit harrowing. You'll have plenty of time to explore Europe once you are settled in. Also, the Swiss Int'l one way prices are outrageous, so you would need to buy a round trip and toss the return.

You don't mention budget. You could redo a trip I did at the age of your older child.

If entertainment for the two very young children is the priority and how long it takes is not, why not take Amtrak across the continent to New York City and take the ship (I think it is the team of Queen Victoria and/or Queen Elizabeth these days) across the puddle to Southampton or Le Havre. Train(s) from there to Milan and then to your final destination. No jet lag and no ouchy ears.

And entertainment by the bucket-load.

I agree with the above replies. Just go from SFO to MXP with whatever airline has the cheapest price and fastest route (which will probably be changing in Europe rather than in the US, as Roberto says). Once you're settled in Varese, you can then take all the trains you and your children want or need. But I wouldn't want to do that on arrival, so flying to Zurich, even though nonstop, would not be as good as connecting to MXP. Remember that when you connect planes all on one ticket, the airline transfers the checked luggage, so all you have to wrangle through the connecting airport is the children and the carry-ons (which will be plenty). But if you go from a plane to a train, YOU have to wrangle everything yourself.

For comparison, I recently took an Amtrak train from New York to Philadelphia, then a local SEPTA train from the station to the airport, then a flight from Philadelphia to Rome. I did this because the flight ticket cost half the miles that a New York to Rome ticket would. And this went fine. But I was traveling alone and could handle all my luggage myself. Also, I have traveled through these train stations many times, knew where to find everything in them (including bathrooms and elevators), and knew alternate routes (if, say, either Amtrak or Septa were on strike). Having just done this, there's NO WAY I'd try it with a 1 year old and a 5 year old, even to save some money.

EDIT: I was cross-posting with Nigel, and had a similar thought. The California Zephyr from San Francisco to Chicago is supposed to be spectacular (2 nights, 3 days), then you take the Lake Shore Limited from Chicago to New York (overnight). With a family sleeping compartment, it won't be cheap, but all meals on the train are then included. I want to do this trip someday myself, when I have 4 days to cross the country, as well as the requisite funds. If you're interested, here's some more, from The Man In Seat 61: http://www.seat61.com/UnitedStates.htm#Crossing%20the%20USA%20by%20train

As you can see, your OP is confusing even to people who have been to Europe dozens of times. It's kind of like asking what is the "best" downtown walk in San Francisco.

Since you did not invoke cost, I would mention that Emirates now flies to Milan from JFK and maybe? Chicago. Their Business Class is unbelievable, and their First Class might be perfect for a family with babes in arms. In JFK, Business Class might enter the plane directly from the Imperialist lounge, with hot food buffet available while waiting.

I can tell you that my parents took me to Europe in 1952, when I was one year old. I don't remember any of it, and it did not inspire me with a love of travel. I developed that later. Supposedly the Italians pinched my cheek and cried, "Belino bambino!"

p.s. As you are going for such a long time it is worth remembering that you can take lots more luggage on the trains than on a plane, and on the ship you can take all sorts.

When I was but a boy we used to cross the Atlantic almost every year, twice in some. We used to take all sorts, often 2 or 3 trunks as well as cabin luggage.

One other thing, the first of those many journeys that I can actually remember anything of was in 1959 or 1960 when I was approaching 10 years old.