6 days in Tuscany - should we split our base

We've done it both ways. Two years ago we spent a week in a farmhouse outside of Cortona. Before we chose where to situate ourselves for a week, I plotted on google mapes all the possible destinations sites and potential lodging sights. The maximum I wanted us to drive one direction was 45 minutes (1 1/2 hours round trip). So I decided on Cortona as it was 45 minutes from Siena, 30 from Montelpulciano, 90 minute train to FLorence (we were 5 minutes from the train station near Cortona), then with days we spent locally, it was a perfect week! In April we spent 3 nights in Montalcino and did everything locally, then drove to Orvieto for a few more days, then train to Rome, then Sorento.
Google maps is a great tool to plan your trip, especially if you are driving so you can estimate driving times. At a glance, if you stayed in Todi, you could easily day trip to Assisi and Orvieto, but Montepulciano and Val D'Orcia would be too much time in a car for my taste. As a suggestion, you could drive from Venice to Montepulciano for 3-4 nights, visit Val D'Orcia, Siena, Cortona, then to Todi for 3 or 4 nights and visit Assisi and Oriveto. You may consider dropping your car off in Orvieto (maybe spend 1 night) and taking the train to Naples, then to Sorrento, which is what we did last trip.

I sometimes like to move just to experience a few more places, especially if it is a first trip to a country. I have gone and stayed in the same place for a few weeks and done day trips, but that was once I knew the area and felt I had chosen the best location. With a car, and in /Tuscany, it's pretty easy to make a quick move.

Driving on country roads in Italy can be surprisingly time-consuming to us Americans. For example, we've had 50 mile drives take 2 hours.I suggest plotting your routes on viamichelin to see how much driving you'll be doing if you use just one base. Be sure to add some time, as most people find the viamichelin estimates overly optimistic. Some say realistically it's 25% more.

I have a computer application called Microsoft AutoRoute. I use it to plan my driving trips in Europe. Enter your destinations and travel specs and you get directions,times and distances. Great program. Google it.

Todi is not in Tuscany, it's in Umbria. And so are Assisi and Orvieto. So Todi is a good choice to visit Umbria (Perugia, Assisi, Orvieto, Spello, Gubbio, Spoleto etc.), since it's also close to the Roma-Cesena freeway. To visit the Province of Siena (Val d'Orcia, Siena etc.) from there, you need to travel 2 hours each way. So take that into consideration. Two lane country highways in Italy are like their equivalent in the US. You can't drive that fast on them. Also Tuscany and Umbria are very hilly and mountaneous, therefore roads can be very curvy too (freeways go through tunnels). The rule of thumb I use is 50 km/h (31 mph) average on country roads and 90-100 km/h (55-60 mph) average on freeways. Assisi and Perugia are mostly freeway driving, therefore they can be reached quickly from Todi. But Montepulciano and the Val d'Orcia are a certain distance from the closest freeway, therefore you have a long stretch of country roads.