The Mahanay Memorial Carillon Tower in Jefferson in definitely worth a stop when traveling to Greene County. Admission is $3.00 for adults and free for children. Inside the tower, you take an elevator to the 14th floor observation deck. There are binoculars available to borrow and the views are outstanding, including views of rooftop art.
One of my kid's favorite parts of the visit was being able to press a souvenir penny at the end. The tower is located just steps from the courthouse and the square has many shops and restaurants to check out. Most are closed on Sundays, but Junkyard Cafe is open and a short walk from the tower.