What is a must do with one full day in Zurich in April? Also, best way to get to Florence; I’m assuming by plane.
when? what do you like to do? The only must do is what you want to do.
I'd take a boat ride on the lake. Others may have alternate suggestions such as going to Luzern or Bern for the day.
I'd take a quite fast direct train to Milano Centrale and change for a fast train to Firenze SMN.
You could do the whole trip on Trenitalia (the Italian national train company) Frecciarossa trains.
Go to the Lindt Chocolate factory for a tour, take the bus to and the boat on the lake back. Visit the Swiss National Museum. If you’re a soccer fan, visit the FIFA museum. Hire a city guide for a tour of the old part of the city.
According to SBB.ch it is six hours or so to Firenze through Lugano and Milano Centrale. That is my limit on taking a train versus a plane... But the trip will be beautiful.
Chagall Windows in the Frauenkirche, Zurich lake boat ride, Swiss National Museum, Kunsthaus Zurich ("As the largest art museum in Switzerland, the Kunsthaus Zürich offers attractive exhibitions of international calibre and one of the most important art ..".).
https://www.nationalmuseum.ch/en
https://www.zuerich.com/en/art-culture/museums-and-galleries/art-museums