Looking for reasonable accommodations for 3/4 days in each of the above hopefully within walking of significant sites
We trusted Rick Steves with two of the cities you name, and found both to be reasonable and comfortable.
Both have air conditioning.
Rome: Hotel Nerva - small refrigerator in your room. Very tiny bathroom, but it's all your own. Within an easy 6-block walk from the Colosseum, and literally next door to part of the Roman Forum. Good breakfast. Just up the street is Mario's Ristorante, which we enjoyed for dinner two nights in a row. Last September, we paid the "Rick Steves cash discount price" of 109 Euros/night and enjoyed our 3-night stay very much.
Florence: B&B Il Bargello has probably spoiled us for bed-and-breakfasts anywhere else in the world. They only have 6 rooms to let, and since Rick put them in his book you may have difficulty getting a reservation -- contact them NOW. Run by Gabriela (a Canadian expat) and her assistant Alison (from the U.S.) -- they were delightful and so helpful. Try lunch at Gusto Leo, which is to your left as you exit the Il Bargello -- we had lunch there 3 times -- pizza, salad, pastas, and dessert were great there, and be sure to try their house-made Sangria. Back to the B&B -- you share a living room & kitchen with the other boarders, and the lovely breezes come through the windows at night or you can take drinks or gelato up to the rooftop terrace to listen to the bells. Three short blocks from the Duomo. In September 2009 we paid the "Rick Steves cash discount price" of 100 Euros/night for 5 nights. We never wanted to leave this place.
There were 4 of us on this trip, by the way, so we experienced two rooms at both
Hotel Centrale in Florence was great. We found it in Rick's Italy book. Gulliver's Lodge in Rome was good (also from his book). Pretty close to Termini and near the Colisseum, located on Via Cavour. Both were in the 120-135 EUR range I believe. Good luck!
For Rome you can't beat Kate at Hotel Giardino (RS recommendation). We are strong walkers and also took public transportation without any difficulties. Close to the Colosseum and the Pantheon. Enjoy!