Where could we go by train for 2 nights before returning to Venice?
If you do not want to venture too far, Verona and Padua are close. If you want to venture further, then Bolzano and the Dolomites for mountains and an Alpine/German flavor, or to Ravenna for Byzantine/Italian. Of course by fast train Florence is not too far.
Verona, Ravenna, Vicenza each have enough to occupy two nights, and the train ride to Venezia is not that long from any of them.
Padua (Padova) and Vicenza can easily be done as a day trip from Venice. Just some 30 to 45 mins away on frequent direct trains.
Ravenna is too far away for day tripping (2,5 to 3 hrs). You could consider staying in Bologna, one of the most agreeable of the large Italian cities, and do Ravenna from there (1 to 1,5 hrs).
You might not have thought of Trieste. A undeservedly undervisited gem of a city, with an almost unspoiled nineteenth century centre. Only 2 hrs from Venice.
Use www.trenitalia.com/tcom-en for schedules and prices. (Use the Italian originals for city names.)
Padua, it's close and has a fair number of things to see, good restaurants.
Here's another vote for Padova. Ravenna is too far.
Thanks for the quick response and good advice! Very much appreciated that you take the time to respond.
I understood that the OP is looking for a place to spend two nights, not a daytrip; if that is correct, Ravenna is not too far.
I agree that Padua or Trieste would be good places not too far from Venice.