From Venice to Milan by train

Padua (lively university town with more than a full day's worth of sights, depending on your interests), Vicenza (smaller), Verona, maybe one of the lakes. Bergamo is an atmospheric hill town on a minor railway line.

I'm not suggesting that you go to all of those places, but those are obvious possibilities.

I have never traveled to Europe in March and don't have a good sense of what the weather would be like. If you're unlucky, Padua has more indoor sights than some of the other options.

You can easily visit Padova (30 minute train journey from Venice), Verona (1.5 hours from Venice) and Lake Garda ( 15 minutes from Verona). You can base yourself in Verona then take the train to Peschiera Del Garda. Once in Peschiera, you can take a ferry and visit some of the lakeside towns such as, Garda, Bardolino, and Lazise.

Enjoy your trip!

Edited to add:

You can check train schedules on Trenitalia.com and you'll need the names of the stations in Italian as follows:

• Venice = Venezia S. Lucia
• Padua = Padova
• Verona = Verona Porta Nuova