11 days by car is a great time to enjoy a trip from Rome to Tuscany 🙂 That route is extremely fascinating and full of things to visit, and your plan to make 2 bases is great as well. Here is the road trip I suggest on the way from Rome to Florence via Siena.
As you’ve already done Florence, I agree with you to make Siena your 2nd location, from where you can go exploring all the classic attractions located on the northern part of Siena; Volterra, Pisa, Lucca, San Gimignano, Monteriggioni, and Chianti.
For your first home base, I would suggest 2 different locations to choose from. The one I most like is the Val d’Orcia area south of Siena and south the Crete Senesi. The fascinaing villages of Pienza or Bagno Vignoni would be perfect.
Another possible location to use as a base would be Cortona, splendid hill town of Etruscan origins that might serve to explore not just Tuscany but also some great sights in the Umbria region. Here is a list of the best day trips to enjoy from Cortona.
Before reaching your first base also take the chance to visit Orvieto, Civita di Bagnoregio, and Pitigliano. You may visit Orvieto and Civita di Bagnoregio on the first day leaving Rome, and then visit Pitigliano and the stunning Sorano and Sovana on a day trip from Val d’Orcia.
Feel free to post any other question!
Enjoy your Trip,