On our first family trip to Italy, we spent 10 days in Portogruaro, a beautiful town in eastern Veneto. From there we took very easy day trips to Venice (2), Padova, Verona (2), Treviso. We also spent a few days just in "our own" little town. The train station was an easy walk from our apartment and the regional trains ran very frequently. Ok, we stayed overnight in Verona so we could see an opera in the arena, but it could have been a day trip if we hadn't wanted to stay out so late. We also had lousy food and were doused in spilled coca-cola in Venice...I will work harder at finding good places in advance next time. I'm sure they exist.
This was in July, and Venice was unbearably hot and crowded, so we were very glad we weren't staying there. In November, you could definitely stay there if you prefer. I applaud your idea of a single region/single base for your trip. We've done that several times (Veneto; Piedmont; Umbria) and have been very pleased not to be on the go every night.
As to the "right" choice of base location - there isn't a wrong one as long as it has a well-connected train station and you find an appealing place to stay. If you're in one place for a week, a kitchen and washing machine is a great advantage. Padova is lovely, as is Treviso, and we had great meals in both towns.