Venice is one of the world’s top cultural cities - major architecture and art all over the place. A day trip is pointless, you will see only a tiny fraction and will get cultural indigestion in the process. Give it time or do not bother, enjoy Verona! A week, a month or several years in Venice and you will not have exhausted its variety.
The best time to visit Venice from November through March. You may encounter fog, rain, or the high tides called acque alta, but mild and sunny days are also common. Air fares and hotel prices are lower, too - which means you can allocate your travel budget over a longer period and give Venice the time it deserves.
There are frequent trains from Milan to Venice. The travel time is about 2 and 1/2 to 3 hours. Just be sure that you’re booked to Venice’s Santa Lucia station, not the mainland stop of Venezia-Mestre.
Some places to go are the Piazza de San Marco where you can see St. Mark’s Basilica and Murana Island where they make beautiful Murano glass. I wasn’t there for Carnivale, which Venice is known for but I hear it is a great place to be if you like big parties. Carnivale is where both Mardi Gras in New Orleans and Carinval in Rio originated from. Things to pick up are their famous Carinvale Masks to wear and of course Murano glass.