I did the Hotel Tritone over in the Mestre area last time I visited Venice. While not in the actual island and on the mainland it is rioght across the street from the train station which is just a nonstop train ride away from Santa Lucia (the train station in the island). There are also bus links to the island. Rates were good and it was close enough to venice and nearby islands. The train station does get a bit shady after dark with some interesting characters.
In Rome I did the Hilton Rome, while it is a great property it is too far way from the sights. You have to take a shuttle which is complimentary to downtown.