We are attending a fixed tour singing with our choir in Rome, Pisa, and Florence. We are considering extending our stay for a week or so after Jan. 4. What area should we concentrate on considering the weather in January? I would love to do Cinque Terre, Genoa, and Milan or the central lakes area, but am very concerned that the weather would be very cold and miserable. (We have already visited Pompeii, Naples, the Amalfi Coast, Venice, Asolo, Veneto, Verona, and the Parma region on our foodie's tour last summer).
Cold and miserable is correct. I would not bother with either Cinque Terre or the lakes. Any cities or towns would work. The rest of Tuscany (Siena, Volterra, S.Gimignano etc.) and Umbria (Perugia, Orvieto, Assisi etc.) come to mind since you will be already in Central Italy (you mentioned Firenze, Pisa, Rome).
If you are skiers, do as the Italians do and head for the mountains. With New Year out of the way, the mountain lodging rates will be rock bottom. If skiing isn't your thing, Cortina can still keep you occupied for a few days. Take run on the Olympic bobsled track. Its 60 seconds of terror (you'll have club members steering and breaking, you'll be practically bolted into the sled). The Passagiata there is a fur coat fashion parade. Venice can be almost tranquil that time of year.
Can you give me an idea of what not to miss if you had 5-7 days to wander in Tuscany and/or Umbria? Is this possible to do without renting a car?
Yes it is possible to do Tuscany and Umbria without a car. If you are in Florence, you can easily do day trips using public transport to the following: Siena (bus/train), San Gimignano (bus), Arezzo (train), Lucca (Bus/Train), Volterra (bus), just to name a few of the most famous Tuscan cities and towns. In Umbria, from Perugia as a base, you can visit Perugia, Assisi, Gubbio, Spello. All within 1 hr from Perugia. On the Florence-Rome train line you can visit Orvieto. Todi and Spoleto can also be visited by bus or train in Umbria. North of Florence you can visit the city of Bologna (37 min from Florence by train). You can also go to Pistoia and Montecatine Terme (Spa), near Florence. Lots of choices, no car needed for any of them.