Hello, I'm from Firenze, so first of all WELCOME TO TUSCANY!!!
I have checked flights from Washington to both rome and firenze at that time and are around 1100 euro. If you don't want to spend time in rome I'd suggest you to fly directly to Firenze or Pisa.
Then, depending on what are your plans, these are my suggestions:
1) Visiting towns like Firenze, Lucca, Pisa, Arezzo: you the train, cheap and efficient (but take 1st class tickets)
2) Visiting Siena: go from Firenze by bus, easier
3) Visiting the country side: rent a car as internal transport are not very good, especially in weekends and it worth to have your own car when driving in the chianti area
Have a safe trip!!!