Suggestions other than Florence or Venice for 7-10 days

If you do stay in Verona, hop over to Padova for a day, also, to see the Scrovegni Chapel (need a reservation) and St. Anthony’s Basilica and the small art museum.

Verona is a bit light on museums, but offers the convenience of being a transportation hub, Brescia, Mantova and Padova are easy and short hops. Mantova, for example, would have more to offer on the arts and architecture side, but is hopelessly sidelined on train lines so maybe Verona is a better option.

Vicenza is a treasure trove for the architecture of Palladio, among which the famous villa »La Rotunda«.
Staying a few nights in pleasant Mantova gives you the opportunity to take the bus to Sabbioneta, a 16th-century »ideal city«.

The Amafi Coast seems like a great spot. Beautiful views and a great hub for travel by taxi or ferry to Pompeii or Sorrento or Positano. Naples is a hub of travel and is an easy location to get in and out of, just don't stay there. Go to the island of capri for a day and the blue grotto.

Why not look into Bologna? I'm trying to fill in some days for our trip next year, and am contemplating doing a 'great food' tour and hitting Bologna, Parma, Modena, Reggio Emilia. We had a half day in Bologna on our first trip to Italy and I've been meaning to get back someday.

Agree with the others about Verona. It's a very good place on it's own, and it is very easy to do day trips from there to Padova and Vicenza.

For something completely different, consider Torino in the Piemonte. It is often overlooked by North American tourists but has a treasure trove of Savoy history, amazing palazzi, wonderful food, the amazing Egyptian Museum and the National Museum of the Automobile. You could easily pass 4 or 5 nights in Torino and it is an easy day trip to Alba or Asti in the wine country, Courmayeur in the mountains, or perhaps Milano. Milano could be worth 2-3 nights for you as well if you have not been.

There's simply nowhere like Florence for art and architecture. I suggest Bologna for something different - it's got a few sights, but nothing major, so it's not a big tourist destination. I really enjoyed exploring it. The big benefit is that it's a rail hub, so it is a great base for day-tripping to a lot of places you might not want to spend more than a night or two. I stayed in a hotel that was about 1/2 way between the central piazza and the train station - 10 minutes' walk to either.

You might consider Volterra in the hill country of Tuscany for at least a few days. Hilly, but walkable, in a city that is many centuries old with ancient Etruscan art in a fine museum and working artists throughout the city who will show you their craft.

Would you consider staying 3 nights each in Parma, Bologna, and Ravenna --- all connected by easy train trips with Milan and with each other? If so, I could tell you more about our Emilia-Romagna trip without a car, staying 4 or 5 nights in each place.

If not, I would say Siena fits all of your criteria easily --- we just spent 5 nights there in early April (having previously stayed there for 2 nights) and could happily have stayed another 3 nights.

Nope, no place is like Florence. Or Venice.

Thank you all for taking the time to respond, and for your thoughtful answers. Lots of great suggestions, and definitely helps with the decision making process. I really appreciate the insight and assistance!

I hope you will let us know what you decide!