That's a pretty aggressive days 3-6.

We really enjoyed Florence during our trips to Italy. While we found some relatively cheap places to stay in Florence, I wouldn't consider it cheap overall. It'd be a pretty tight one day if you want to see all the biggies like the Duomo, David in the Accademia, and the Uffizi. The core of where you want to be is pretty compact so everything is withing walking distance. We also really loved the market and the food in Florence.

Our friends loved Milan and revisited it during a second trip to Europe. We haven't been. It'll likely be on our next trip to Italy but we'd probably want to package it with Lake Como.