I agree with shelby. In Florence, stay in the Duomo area, which is the center of the Centro Storico. Most everything you'll want to see is just a few minutes walk from there, and since the area is closed to automobile traffic, you won't have to dodge cars every two seconds - just those darn Vespa's. The area around the train station is pretty noisy most of the night, and a bit iffy too. It's also features places like McDonald's, so it's definitely not as picturesque at the center of old Florence.
Two wonderful hotels I've stayed at and can highly recommend (both within minutes of the Duomo) are the Helvetia e Bristol, which is at the front of the Palazzo Strozzi and just one street over from the best shopping street in Florence - Via de Tornabuoni.
The other is the Hotel Lungarno (owned by the Ferragamo family), which is situated on the other side of the river, the Oltrarno, but it's only minutes away from the center of Florence and just maybe a hundred yards from the Ponte Vecchio.
Wherever you stay, be sure to eat at Quattro Leoni (also located in the Oltrarno) and be sure to order the Fiochetti da pere con salsa de tallegio e asparagi (little pasta pouches filled with pear and cheese and served in a white sauce with tallegio cheese and fresh asparagus tip - so delicious.) They're open for both lunch and dinner.
And, if you truly want to experience the magic of Venice, I think I'd try to avoid staying in Mestre (it's somewhat dreary and industrial) and stay in one of the five Venetian districts instead. San Marco is the most central but also the most bustling and most expensive, but I had a very enjoyable stay at the Hotel Giorgione in Cannareggio, which is just a short ride on the vaporetto to Piazza San Marco. They also include a huge and very good breakfast in the price of your room.
And another advantage of staying there is that it's just a brief walk to one of my very favorite Venetian restaurants, Vini da Gigio. It's a small family-run place, which features excellent pasta and meat dishes, which is a nice change once you get tired of seafood, which, of course, is a Venetian specialty. The address is Fondamenta de la Chiesa, Cannaregio, and it sits right on the banks of the San Felice Canal. The phone number is 041-5285140. Reservations are pretty much a must, as it's small and very popular both with Venetians and tourists alike.
A hotel in Rome that my sister highly recommends is the Albergo del Senato on the same piazza as the Pantheon. They have a wonderful rooftop terrace where you can enjoy drinks and meals overlooking the dome of the Pantheon. She said that the rooms are fairly small (they usually are in Italy and most of Europe anyway) but very well furnished, and the staff is lovely and very accomodating. I think they have a website if you're interested. I'd certainly avoid, Termini, though, as that's where the large rail station is located, and it can get pretty "iffy" at night. Do you think that they could have meant to say Trastevere instead?
Regardless of where you decide to stay, have a wonderful time!
Thanks Shelbygirl, Lilyhermes and Duna 
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