Milan as home base

Milan for one month is a bit much.

Yes, staying in one place simplifies things for your lodging, but you waste a lot of time in transit to where you go.
I can see Milan to visit Switzerland and Northern Italy to some degree, but not for a month.
Do your research and determine where you wish to visit and WHAT you wish to see.
I have traveling all over Europe and used the trains quite a lot. Italian trains can be late, especially the regional trains.

Check out places like Lake Como, Lucerne, Interlakken, Lugano for Switzerland. Geneva might be too far, but determine how long it would take to get there. There are many scenic places in Switzerland that are a bit remote and not large cities.
As for northern Italy, Venice might be too for to visit, but Genoa, Turin, Bologna and Verona are possibilities.

Consider two weeks in Milan and two weeks in Tuscany and/or Umbria.

Also rethink the Eurail Pass. That is rarely a useful thing to have in Latin Europe. Something tells me that you are not very familiar yet with trains in Europe.

Note that there are no places in France, Germany or Austria that are within day trip distance of Milan. The only place as you could conceivable visit are a few in Switzerland.

This is very helpful feedback, thank you all! Definitely inexperienced travelers here and in the very early stages of planning. We should also clarify that we’ll be traveling with an 11-month old at the time, so that’s especially why we considered staying in one location to avoid having to transport luggage, portable crib (because most AirBnbs don’t provide these), stroller, supplies, etc. I’m open to sticking to one country (Italy) to explore it in more depth, but what would be the most effective way to visit multiple countries within a month span? Should we jump “home bases” every week or so? We’re also trying to stay cost-effective, and AirBnBs seem to have the best deal when staying for longer periods of time.

I’m open to sticking to one country (Italy) to explore it in more depth, but what would be the most effective way to visit multiple countries within a month span? Should we jump “home bases” every week or so? We’re also trying to stay cost-effective, and AirBnBs seem to have the best deal when staying for longer periods of time.

I understand with a young child the desire to have home bases. Shorter day trips might be a good idea as well.

If you want to visit multiple countries, I’d suggest a week in each of four places at most.

Sounds like Italy might be the leading edge favorite so perhaps a week in Verona or Padua, smaller cities between Venice and Milan, allowing some nice day trips in the Veneto.

If you choose to stay in Italy, another week could be in Siena or Florence, easy to get to by train. Day trips in Tuscany by train are a little limited but bus service is good. If you base in Florence for a week, you can visit Lucca, Pisa, Cortana and more, plus allow several days for Florence itself. Then maybe head south to Assisi, Orvieto, Rome… If you really plan to stay in Italy, let us know and you’ll get many ideas.

If you want to go to other countries from the starting week in the north I suggested, Luzern, Switzerland may appeal. Easy enough to get to by train (4.5 to 5 hours). From Luzern there are many day trip options by train and it is a lovely city.

From there, perhaps you can consider going to France or Germany.

I agree an AirBNB or VRBO or other vacation rental (Booking.com has them, too) is efficient and economical for a family. Eating in helps the budget and the baby’s schedule, having separate spaces is nice for a longer stay.

I am widely against AirBNB and Co because abusing housing space for renting to tourists created real bad housing situation for poorer families in a lot of twons and locations in Europe.

What's creating the housing shortage in certain European places is the lack of new construction to meet the demand. The localities that suffer from this problem need to incentivize new housing rather than discouraging it.

I've studied this issue at some length. And I acknowledge that your anti-business attitude has, in this instance, a kernel of validity; some landlords indeed have converted former long-term rentals into short-term, often at the expense of local citizens seeking decent housing. But a kernel is all; too many European cities and even nations have erected barriers to new construction that have greatly harmed citizens seeking affordable rental housing. Pretending otherwise betrays a socialist credo that the market is a bad thing and the state should control commerce.

Your suggestion that "building new multifamily housing makes no sense" at a time of housing scarcity itself makes little sense. It's like claiming the solution to hunger is to stop growing food.

As a final remark, I'll just note that I know a couple of multifamily developers who are avid Europe travelers, and who saw an opportunity because of the housing shortages in several European cities (in their cases, Italy). They did some initial due diligence to ascertain feasibility, but fairly quickly abandoned their projects. The reason? Bureaucratic delays, barriers and impediments made the effort unworkable.

Just as a rule of thumb. In my opinion day trips should not exceed a two hour one way train trip. Leave by 8:00am or earlier and return after dinner. Daily day trips will take its toll on you after a few of them in a row. If you are traveling for a month, at the minimum, have a home base in each of your selected countries if day tripping is your plan of travel.

It is natural to seek a variety of cultural experiences on a one-month trip. However, you don't necessarily need to leave Italy to accomplish that. There is a lot of variation among the various regions in Italy. There are towns in the Alto Adige/Sud Tirol where German is more widely spoken than Italian, and the food shows a significant Austrian influence.

Options for practical daytrips heading to countries north of Italy are limited to non-existent because of the mountains blocking the path. Those train trips are not very fast. You can explore the logistical challenges on the Italian (trenitalia.com), Swiss (sbb.com) and Austrian (oebb.com) websites. There are other parts of Europe where it's easier to take short trips across borders.

Switzerland is a beautiful country with a well-engineered rail system, but it is a very expensive destination from the standpoint of hotels, restaurants and rail fares (per mile).