I've been to Florence, and while I love South Carolina, I wouldn't stay a week
I would love to have gone to florance when in Italy this past summer, but also wanting to see the town / area my Grandparents came from kept us in Southern Italy. I'm also not generally into the major tourist traps unless I have a lot of time, which we didn't.
We spent much of our time in Sorrento, and it's quite affordable. It's a popular tourist spot, but not as crazy as most. From Sorrento, we visited the Isle of Capri, which is one of the most beautiful places I've ever seen. We also visited Naples, and spent more then a full day just in Sorrento. They shut down the main street in town at night so people can go out walking. Very cool place.
We stayed at a small hotel in the hills just above the town so we would have some nice peace and quiet. Hotel Il Nido. It's rated one of the ten best bargins in Italy by Trip Advisor, and we really loved the place. They don't have a pool, but that wasn't an issue for us. The staff was outstanding, and stayed on duty long beyond normal hours while we sat on the terrace with some other guests. Food was great, and I'm an eater, and Italian, so trust me on this one.
There are many great deals in the Sorrento area. You can do day trips to Rome and other destinations from there.
Check out my blog on the Noosphere. I added it into my motorcycle blog, but it goes from the planning stages through the entire trip. Lots of pics from the trip. We went in late June into early July. Airfare cost us about 2400$. We rented a car, which unless you have some crazy driving skills, and nerves of steel. Train from the airport to the station in Sorrento, and shuttle to the hotel would have been the wise choice if we hadn't planned on driving down to Calabria / Carolei.
If you do end up going to Italy, let me know. I bought a euro power strip to plug all my goodies into at night. I didn't need a converter, as all my chargers will work on US of foreign voltage / Htz. I'll be happy to lend it to you.