Preheat oven to 375 degrees F.
In a medium bowl, with electric mixer, cream butter and sugars together until light and fluffy. Add eggs and vanilla and beat until just combined. Set aside.
Sift together flour, soda, and salt. Add milk to the butter mixture and then add the flour mixture. Mix until just combined. Batter should be stiff.
In another bowl, combine nuts, cherries, and white chocolate. Then add to batter, stirring only to blend. Drop by heaping tablespoons onto a greased cookie sheet, 2 inches apart. Bake for approximately 11 to 13 minutes. Cool on wire rack.