7 to 10 days independent before a northern Italy tour

I love Vienna and if you haven't been there you should certainly consider it. If you rent a car you can easily see some other sights, like Salzburg, Munich, the Dolomites, Verona and then into Padua.

I would fly into Milan and spend 3-4 days at Lake Como and then work my way to Padua over the last 3 days. Lake Como is just a special place that makes you feel good about just being alive. I love Italy, I hope you have a great time!

the RSE Northern Italy tour,

Had to look through the tour list to find RS calls it "Village Italy"

We have spent a lot of time in Northern Italy and love it. We have been to Vienna twice and have no desire to return. I also prefer not to mix countries on a trip.
If you fly into Milan MXP you can rather easily travel to the beautiful, under touristed Piemonte region, base in Alba, or head down to Liguria to Santa Margherita Ligure or Camogli. And then there are Bologna and Verona.. It is also easy to travel to Lake Como or Lake Maggiore( close to MXP) from Milan. Each of the Italian Lakes are different from each other. You have been to Florence, but what about smaller towns in Tuscany like Greve, Panzano, Radda, Pienza, Montalcino or beautiful Siena?? Or in Umbria such as Spello?You have so many wonderful places to choose from. Do spend a night in Milan to see the Duomo and get tickets far in advance for da Vinci's "The Last Supper." Antica Locanda Leonardo is nearby and is a nice, quiet hotel. I would gladly return to all the places I have mentioned in Northern Italy.

Wein/Vienna is a great city. Since you have a good amount of time before the tour, spending time in Austria before hand sounds fun. Then you could fly or train to Venice and train to Padua to start the tour.

If you’re taking the RS Village Italy tour, I would either visit the larger cities in Italy during your independent time, or spend that time in Austria as you suggested.

Italy- all of these are easy by train. # of days are just suggestions
fly into Rome (3 days)
Florence (2 days)
Torino ( 2-3 days)
Verona ( 2 nights)
Quick train ride to Padova.

Austria
fly into Vienna (3 days)
St. Wolfgang (2 days)
Salzburg (3 days)
Flight to Padova or Verona or train & stop at Bolzano area

As Horace Greeley said “Go west young man.” I highly recommend Torino and if you would rent a car, a few days touring the Piedmont wine country around Alba - Barbaresco, Barolo, Asti. And/or drive the local roads through Val d’Aosta to Courmayeur and take the Skyway Monte Bianco to the top of Mt. Hellbronner. A friend and I were in that area last year in late September and it was spectacular and not mobbed with tourists.

Assuming 10 nights, and taking into account the stops on your tour, this is what I'd do.

Fly into Milan, go directly to 3 Varenna on Lake Como. 3 nights.

Back to Milan 1-2 nights.

Then train to Bolzano and bus to Ortise in the Dolomites 3-4 nights.

Finally a train to Padua.