Preheat oven to 350 degrees F (175 degrees C). Lightly grease two 9 inch round pans.
Combine sugar, flour, baking soda, water, mashed bananas, salt, and mayonnaise. Mix together, and pour into the cake pans.
Bake cake about 45 minutes, or until a toothpick inserted in the center comes out clean. Remove from oven, and cool on wire racks.
In a mixing bowl, blend cream cheese and butter or margarine together. Gradually add sugar and vanilla, and mix well. Stir in nuts. Fill and frost the cake.