Well if you are going to venice I am thinking visit the grottos and the hand blown glass places. If you time your trip to venice properly it is a good day trip. I think you have to ride in by boat. Be prepared to do a lot of walking around. The tides there may have damaged a lot of areas that were at one time quite nice. I was there once and went to the leaning tower of Pisa and the church in that square is quite historical. Think Indiana jones. When I was there 30 years ago you could still climb the stairs at the tower of Pisa. Maybe churches are not your thing.
As far as Rome goes, there are so many places a tourist could go and so many places to eat. Lets see Castel Sant Angelo, and the Basillica are pretty close. Outside is a big square with a Obelisk. The Colloseum, The vatican. More ruins than you can imagine. Then there are the fountains. Trevy fountain is nice on a hot day. You could write a book just on the fountains of Rome. Near the Trevy fountain is the spanish steps where there were always people selling stuff on blankets in the street. There are some German restraunts near there. There is an old Roman cobblestone road from Rome that heads towards ciampino where the old internetional Airport was. It is like paved over now but you can see the old dark grey stones showing through in places and the sides are littered with some old ruins. It was very picturesqe. Ciampino is not that special but it is half way between Rome and Frascatti. Frascatti is an older city with fountains and it is up in the hills. Many little towns around Rome are up in the hills surrounding Rome. Frascatti has some nice restraunts, a monestary where they make their own sausage, and they have a festival there where they use to have wine coming out of the fountains.
If you know where to go there are so many interesting places to go to in Italy. I tend to like the out of the way places and the small towns with their old-style restraunts. Almost every town or area has its specialties and unique areas. A tourist without a car could see Rome best by using trains and busses and walking a lot. You dont even have to stay in a large city, because you could stay in small hotel and just ride into the trainstation into Rome for peanuts.
In many places in Italy you could travel by bicycle, or scooter. Some of the roads are narrow and the piazzas (Squares) might have things like artists painting pictures. You could also spend an entire day going to the open air shops. Typically most towns had some kind of maret one day out of the week or more.