Anne, I'm also an avid travel Photographer. I discovered during a trip to the U.K. in 2004 that P&S Cameras have some "limitations", so my current kit includes a dSLR with a few extra Lenses. I also carry a small Canon Elph as it's handy to take out at night for candid snapshots or whatever. There have been MANY instances when I've been really glad to have the dSLR, as I've been able to get some shots that wouldn't have been possible with a P&S.
As far as things to photograph, there are so MANY possibilities in the places you listed. As others have mentioned, photography is possible in many Churches and some Museums, but usually only allowed without flash. Also, some locations prohibit use of Tripods.
A few suggestions:
Venice - Piazza san Marco (at night or after a rain), Gondolas, canals, buildings, view of Venice from the tower?
Florence - Ponte Vecchio (esp. at night), Duomo, view of city from across the river, scenes of Fiesole, street entertainers in the main Piazza?
Rome - Colosseum, Forum, old buildings on Palatine Hill, bridges on the Tiber, Isola Tiberina, Pantheon (inside & out), Victor Emmanuel Monument, street scenes in Trastevere, various Piazzas such as Navona or Campo di FIori, Trevi Fountain?
Cinque Terre - villages both from land and the sea, trails, buildings, people, harbor areas & boats?
Sorrento - view of city from the surrounding hills, harbour areas & boats, street and people scenes, cruise ships in the bay?
The Borghese Gallery is VERY strict about photos! Visitors must check any kind of bags, purses, backpacks etc. Even if one had a Camera in a pocket, there are guards in each room and CCTV everywhere. The Borghese gardens next to the gallery are beautiful and a good photo op.
St. Peter's allows photos as I recall. The view from the top of the dome is fantastic (especially looking toward Castel d'Angelo).
Congratulations and hope you have a wonderful trip!