So far I see
Rome: 5 nights
Cinque Terre: 3 nights
Florence and/or Siena: 5 nights
Venice: 4 nights (or maybe 5 since it's not clear if you are flying home on June 8th or if you are in Venice that night as well).
You are not specifying if you are willing to rent a car for portions of your trip. But if you like smaller places I would consider renting a car in La Spezia (near Cinque Terre) and drive from there to a small town or a country villa/hotel between Florence and Siena. It will be very relaxing, trust me.
You could visit both Florence and Siena from that countryside location. If you don't care too much about museum, just drive to Florence in the morning, park outside the city walls, and spend all day there. If you think you could visit an extra day, just go back another day and do the same. Siena can easily be visited in a partial day. The rest of the time you can visit the small famous towns and countryside in that area (San Gimignano, Chianti Hills, Monteriggioni, Pienza, Volterra, and many others.
You could drive all the way to Venice and return the car when you arrive (on Piazzale Roma) or you could return it in Florence and from Florence proceed by train to Venice (2h 5 min train trip).
If that is a workable plan for you, then I would even consider a longer stay in that countryside setting. All you have to do is borrow a day from Rome (Rome is a vast city, but 4 nights are sufficient to see the basics) and maybe one from Venice. Three nights in Venice is generally more than sufficient for Venice and the islands (Murano, Burano, Torcello); with 4 nights I would definitely take a day trip to Padua, just 20 min away from Venice.
If you don't rent a car, I would probably stay in Florence, which is the transportation hub and from there you can take day trips to many places, including Siena. In spite of the warnings about Florence being busy and crowded, there are plenty of places, even in the city center, which are very quiet and not particularly overcrowded with tourists, especially considering that the entire city center is off limits to cars. I don't know where the hotel mentioned above on Viale Vittorio Veneto is, because Viale Vittorio Veneto does not exist in Florence (maybe the commenter meant Piazza Vittorio Veneto, which however has quite a bit of traffic during the day).