We're staying in Florence, Sestri Leavnte, Chastellina in Chianti, and Corotona, and plan on doing all of the towns during day trips from these locations. For the last place, we want to stay in Umbria - where would you recommend as the best situated city? Keep in mind, when staying in Corotona, we can probbaly visit a few towns that are on the border of Tuscany and Umbria.
I would stay in Spoleto. From Spoleto, by rental car or by public transportation, you could also visit Norcia, Narni, Amelia, Todi, Foligno, Montefalco, Bevagna, Trevi, Spello, Assisi and Perugia. Even Gubbio is doable via Fossato di Vico in northeastern Umbria.
This subject has been discussed many times, so it is a good idea to use the find button and make a search. Umbria is pretty small but there is lots to see, so in 2-3 days you will only get an impression of the region and most likely you will want to come back!
With a car Susan, your base hardly matters, except that northern Umbria (including Gubbio, Città di Castello) is not so central, and much less inhabited over the centuries, and thus fewer things to see.
Given 2-3 days, I'd sit in one town and poke around. My choice in your shoes might well be Assisi, which is not that great on a daytrip, but magical if you stay there.
But, as mentioned, Umbria has been discussed in quite literally thousands of posts; in this thread, you'll only catch the few of us awake and responsive right this minute, and might miss the bulk of the good information, also representing a more balanced cross-section of opinion — so do use the search ferret.
Somewhat bashfully he adds that his own website is one of the most useful for Umbria information, and should help you make up your mind: