Ha! Sorry, John. The Tuscan-Umbrian rivalry is like New York vs. New Jersey, or Vermont vs. New Hampshire: There are more similarities than differences, but we keep it going for fun. Plus Umbrians are lower-key and think that Tuscans just hog the limelight. And southern Tuscany is almost overrun with Brits, so much that it's nicknamed "Chiantishire."
Should you wander into Umbria, I'd say yes to a day on the lake. Take a morning ferry to Isola Maggiore from Tuoro sul Lago. Hike around the island--you can't get lost--and then have lunch in the garden at Da Sauro. Perugia's a cool college town, worth an overnight. I like Gubbio, Spoleto, Spello and, for reasons totally unrelated to "sights," Gualdo Tadino. And, of course, Assisi. Don't overlook nature walks either. You can duck inside the door on the right in the wall outside Assisi's basilica and take a hike in St. Francis' Woods--Il Bosco di San Francesco. It's a beautiful, tranquil place run by FAI, an environmental group. In general, there are lots of great mountain, lake, and forest hikes in Umbria. And since it's Italy, a good drink or coffee or meal is just around the corner after your hike.