Gene,
Personally, I'm not a fan of hitting a new city for only one or two nights. In your case, I would pick Florence as a base and explore the city and the surrounding area leaving the Cinque Terra for another trip.
If you haven't purchased plane tickets yet, you might want to look into and out of Florence, Pisa or Bologna. It probably won't be a direct flight from the USA but it will save time on the ground and may actually be cheaper. I've flown into Bologna and shuttled to Florence (Bologna airport to Florence S.M.N) for about €20.
In Florence you have more than enough to keep you occupied for a week. I personally don't recommend hitting the Accademia and the Uffizi in the same day because the are so stimulating but I do recommend taking escorted tours if you are not REALLY knowledgeable about renaissance art (I am not).
I wonderful self-guided day trip I can is to Pisa (as early as possible) and Lucca (remainder of the day. While it seems a shame to go to Tuscany and NOT see the leaning tower, it wasn't most satisfying experience I had in Italy. I would take an early train and try to beat the worst of the coach tour crowds, see the Duomo and Tower and then head to Lucca (train or bus). Lucca is wonderful and shouldn't be missed.
Probably the highlight of our week in Florence was an escorted tour of vineyards in Chianti. Great wine, food and scenery and someone else had to abstain from the wine and do the driving.
I hope this helps. Good luck.