My sister and I arrive in Venice in early May, and need to meet a group at Zurich airport 11 days later (to begin a hiking trip in the Swiss Alps). We definitely wanted to re-see Venice, but have no fixed plans beyond that. My sister has never seen Florence, so that may be an option. I'd love to see something beyond those two meccas, if time allows. We will travel by train and bus.. Where would you spend those 11 days?
You could go over to Verona by train. Then take a train up to Innsbruck to see the incredible Alps. And you could catch a train to Zurich from there. (Note: Zurich isn't in the mountains and is not particularly interesting.)
I forgot to mention, we are meeting in Zurich to begin an 8-day hiking trip in the Alps!
If you work your way across northern Italy to Milan, you'll then connect with the main route Milan-Zurich. You'd have time to go south via Ferrara to Bologna, then to Modena, Mantua, Verona, Brescia, Bergamo, and Milan. If you love history in the period of the great ducal families (Este, Gonzaga, Borgia et al.) you'll find Ferrara, Mantua, and Verona irresistible.
Venice 3 or 4 days.
Florence 4 days with bus trip or two to, say Siena or Lucca.
Varenna on Lake Como 3 days, then train over the Bernina Pass ending in Zurich to meet your friends.
Think in terms of number of nights you have. "Days" gets tricky counting the time.