Preheat oven to 325°. In a large mixing bowl, beat butter with an electric mixer for 30 seconds. Add sugars, baking soda and salt. Beat until combined. Beat in the eggs and vanilla until mixture is smooth. Using the mixer, beat in as much of the flour as you can. Stir in remaining flour by hand. Stir in cherries, nuts, chocolate pieces and white baking pieces (dough will be stiff). Drop from rounded tablespoons 2 inches apart on ungreased cookie sheets. Bake 14 to 16 minutes, or until golden.