With the Euro/USD currently at 1.09, thank your lucky stars you' weren't traveling in 2010 like we did. The conversion then was 1.43, plus it was our first trip to Italy and blindly stayed in hotels that were a little too pricey. They were beautiful but in hindsight we didn't need all that much room. You can do so much better now cost-wise.
I am not familiar with Venice, and don't want to give it short shrift, but with only 10 days (9 nights?) to work with, you may be better off flying into Milan Malpensa on an overnight flight, arriving in the morning. Then you would take the Malpensa Express to the Milano Centrale train station and it's 1 hr., 40 min. to Florence Santa Maria Novella (Firenze SMN) station.
Base in Florence for 5 nights at a hotel or apartment within a few minutes walk from the station. You should be able to find a decent hotel for no more than $150/room/night (2 rooms?) or better yet, an apartment through VRBO, AirBnB or HomeAway that sleeps 4 could be found for as little as $100/night. I know this for a fact because I did exactly that this last March. Daytrips from Florence are easy and cheap to Fiesole, Lucca, Pisa, Siena...and Venice. Direct trains to Venezia run all day back and forth, 2 hours each way, a perfect way to enjoy the city without the cost. And just wandering around Florence, not doing anything at all, is a real treat.
The Freccia train Florence to Rome is 90 minutes. Four nights in an area like Campo de' Fiori or Trastevere is a perfect way to enjoy the Eternal City, or even to take a day trip to Pompeii if the mood strikes you. Hotel/apartment prices--depending on the neighborhood--are comparable to Florence. And then fly out of Rome.
With this plan, you're only packing up & moving once during the 9 nights, allowing you time to enjoy what you came for. Only omission is the Cinque Terre, which in early May could still be quite cool.
Enjoy your planning!