I assume you're hitting Rome first? There's a place called
The Beehive which is handy for a few reasons: it's close to the train station, easy to find, and relatively inexpensive. It's run by an American couple, which can be nice on the first night to ease the transition. It's been a few years, but when we visited Italy we stayed there on the first night and then on subsequent nights in Rome moved to an apartment that we rented with friends. I might be wrong, but I think we found the apartment through the beehive's
"Cross Pollinate" site, which allows you to search for guest rooms, B&Bs, and apartments based on the number of people in your party, the dates you want to stay, and your budget per night. That might be a useful resource for you.
In Florence, you can find fairly inexpensive hotels if you want to stay outside the city center, but then you have to hop the train to get to and fro, which isn't terribly inconvenient but can be time consuming. We used the site
Venere to find our place in Florence. (You can also use it to find places in Rome and Venice.) We found a relatively inexpensive room (for the location) through that site at
the Hotel Bavaria. If you don't mind walking down the hall to use the bathroom you can get a double room for around 40 a night. Also, hotels in Florence make it easy to get tickets for museums--you can usually buy tickets for the Uffizi and the Accademia (home of David) through your hotel--it's convenient, guarantees that you've got a time to get to the gallery, and I think it's less expensive that way.
You might be able to find a relatively inexpensive Venice room through Venere too, I don't know. Our traveling companions were responsible for booking our Venice room, and I think they found the place through the listings in Rick Steve's book. It wasn't cheap, exactly, but was relatively inexpensive for Venice--you can find a great deal occasionally, but make sure it's actually on the island and not on the mainland.
Anyway, I may be telling you some information that you already know, but maybe one of those resources will be helpful for you. Have a great trip! :hi: