First of all you need to decide whether you intend to have a rental car at all or if you intend to rely exclusively on public transportation.
Since you've been to Florence twice already I would rent a car and base myself in an Agriturismo (farmhouse) or a B&B in a small town (if you prefer in-town accommodations) located between Impruneta and Siena, somewhere along the Raccordo Florence-Siena freeway. From that location I would do day trips. There is no reason to go to the trouble of splitting your stay. From the area I mentioned nearly nothing in Tuscany in farther than 90 min away by car. Besides, if you want to stay at an Agriturismo, many of those rent only a min. of one week. I would consider splitting bases, only if you want to visit both Tuscany and Umbria. In that case I would still stay where I mentioned for Tuscany, then I would base myself at or near Assisi for visiting Umbria (and do day trips to Umbrian towns from there).
If you fear driving and prefer to rely on public transportation only, then the best is to stay in Florence, Tuscany's capital and transportation hub. For Umbria, if Umbria is also in your plans, you might consider Perugia (Umbria's capital and transportation hub).