Tuscany

I can highly recommend Agriturismo Marciano in Siena. They do not require a one week stay. The rooms are charming, the agriturismo is a winery and they make olive oil. The people are friendly and helpful. The optional dinners they offer the people who stay there is to die for. The best food I had in my three weeks in Italy. Don't just take my word for it...check them out on Trip Advisor. I found it to be a very convenient base to go to hill towns. We spent one day going North, the next day going South, and our 3rd day we spent in Siena. I wish we had spent more time there.

You can also try b&b's. They normally do not have a week long minimum stay. We stayed at a lovely place outside of San Gimingnano. Was a great base. We traveled to Montalcino, Pienza, and Siena. We stayed at a lovely b&b. Il Vicario is located just outside of San Gim. Wonderful hosts, reasonable cost and wonderful cooking lessons and evening meals if desired. Rated highly on Trip Advisor.

What time of your are you travelling? If you are there in the off season you might be able to get a 4-5 day rental instead of a full week even if it's not advertised. I'd contact the agriturismo directly and ask. During high season your choices of places renting for less than a week are much more limited.

We were looking for a villa on VRBO for 6 nights and received a couple of responses back quoting a prorated rate for 6 nights instead of the full week.

Siena is a good base for Tuscan hill towns and Umbria. Easy to get to the hill towns via the roads North of the city, and good roads for getting to Umbria quickly. If you want less travel time, then Assisi is a very nice little town. You could also base yourself out of Perugia.