I was lucky enough to be able to go to Rome for a vacation for 2 weeks. I just got back yesterday (to a wonderful welcome from the cats and dog!).
I found a wonderful cat santuary right in the heart of Rome, called Torre Argentina (web page www.romancats.com ). Over 250 cats live there, and the work these people do is amazing. My fiance and I spent 3 hours there playing with the cats. If you are ever in Rome it is a must see, and it is close to all the major attractions.