I`ve been on a roundtrip of northern Italy earlier this year, one day per destination: Venice, (Verona), Milan, Florence (San Gimignano, Siena), Rome, Bologna.
I have however been to Italy before, so I didn`t
need to see every small little thing.
Since you are a little more pressed for time, I`d suggest you go shopping in Milan, it`s shopping heaven and in my honest opinion, not the prettiest town.
In Florence you need to see the Ponte Vecchio, but you should not necessarily buy any jewelry there, because it`s really not the best quality and almost all of the shops belong to the same owner. Of course you should also see the Dome, the entrance is free. If you walk the few hundred meters from one place to the other you will see some other sights as well, but your best bet would be to check what you are most interested in (Art? Churches? Architecture? A general picture?). I have a very good Restaurant recommendation, but would have to look up the place if you are interested. It was a smaller place, not well known with tourists, very affordable - if you don`t plan to dine in the most exquisite settings, they have amazing food there!
If your trip should bring you by Siena and/or San Gimignano or Pisa, those towns are definitely worth a stop.
For Milan: you will probably end up right in front of the Dome, if you go for a little shopping spree. Then you should see the Galleria, but the Scala is no highlight, it is right behind the Galleria, though, so you can easily walk by that.
I blogged about my roadtrip, but I`m not sure I can link back to that here, so just go check it out, if you want to.
About Rome: I have another very, very, very good restaurant recommendation (affordable, too). The homepage is:
http://www.lapiazzettadetrastevere.com/
You should see the Spanish Steps, Fontana di Trevi (throw in a coin, too!), Vatican City, the Colosseum and the castel sant` Angelo. It`s not the nicest building, but if you go to the top you will have a beautiful view from up there!
These were really just some typical touristy places. Hope you have a wonderful trip!