Drive to the town of Tuoro sul Trasimeno or Passignano--but first look at the ferry schedules. Take the ferry to Isola Maggiore. There are hiking trails throughout the small (despite it name) island. Some are quite steep. At the end of your walk, have lunch on the terrace of Da Sauro, overlooking the lake. Good food, decent house wine and a warm staff. Be sure to reserve.
Another excursion is from the town of San Feliciano. Take the ferry to Isola Polvese--it's an environmental lab. You'll have to sign up for a tour to see what they do. Or you can just walk around the edge of the island; it's just a beautiful walk.