Forget the crowds. You can get around those crowds at the major museums (Uffizi and Accademia) by making reservations online. Also in summer they stay open later and toward the end of the day it's less crowded. I wouldn't spend more than two hours at any museum. The Accademia is small, all you need is the time to see the David and a few more Art works and you are done.
The decision on whether to stay in town or out of town should be dependent upon whether you have a car or not. Without a car, I would stay in the city center, with a car you should stay in some quaint place between Florence and Siena, and drive in to Florence and park for the day while you visit. There is plenty of parking outside the ZTL, including in or around Piazzale Michelangelo, which can be reached very easily coming from anywhere south of the city.
As to the location to stay in the latter case, it's most efficient to stay somewhere along the freeway that connects Florence to Siena. Anywhere between Impruneta (very nice and near Florence) to Siena would work. If you absolutely must stay in Florence with a car, stay along the Viale dei Colli (the boulevards on the hills from porta romana to Piazzale Michelangelo to piazza ferrucci.
If you choose a base closer to Siena, you can even get by with one base only. From Siena you can drive almost anywhere in Tuscany and most parts of Umbria in 90 min or less. Just find accommodations near the freeway, many farmhouses are in the boonies and far to drive too. So choose carefully if you go the farm house route.