Florence was not my cup of tea either, my wife hated it. Rome is crowded with tourists but worth the effort. Florence is similarly crowded but not worth the effort - Although they have a great indoor central market. I stayed at Frances'Lodge, a 5 room B&B just outside of Siena for six days in September. Awesome views, great hospitality, surrounded by olive trees and vineyards and easy day-trips to all of Tuscany by car. Franco has Setters and used to hunt, Franca, his wife, made him give it up. Siena is big enough that you can dine well for a week never visiting the same place twice but neither too big nor too crowded. I'd highly recommend it.
I never did find any bird hunting opportunities but I did see hunters in the fields a couple times while driving. Have fun.