I don't think 8 days is a lot for the Amalfi Coast. I've done three trips there, two of them for about 8 days each and never got bored. If you base in Sorrento you have day trip options to Positano/Amalfi/Ravello, Capri, Ischia, Naples, Pompeii/Herculaneum, Salerno/Paestum. So I wouldn't worry about too much time there.
For the rest of your trip I agree Florence would be a good first stop, then I would do Venice and end in Milan since that's where you'll most likely find the best flight options (flights to the states from Venice tend to leave very early). I would just do those three as 'bases' but there are numerous day trip options from each of them. From Venice there is Padua (half hour, very easy) as well as Vicenza and Verona. From Florence the 'best' day trips are Pisa/Lucca (combined on same day, by train) and Siena (by bus). You can also do organized tours to smaller towns in Tuscany but those are harder to do by public transportation. But Siena is actually a Tuscan hilltown, albeit a big one, but if you take a walk around the 'edges' of the old town there are gorgeous views, and the town itself is gorgeous. From Milano I've day numerous day trips - Lake Como, Lake Lugano, Pavia, Bergamo, etc.
I've done lots of those places as a solo female traveler and don't do anything different than when I'm traveling with my husband or a friend. I perhaps make sure my hotel is good and central and has a 24 hour desk, but other than that nothing different.
Here's my photos of all those places - https://andiamo.zenfolio.com/f739967755
On that same site (under the 'blog' tab) is a trip report I wrote about one of my trips to Venice, Florence and Milano where I mention the names of hotels, etc.