Which of these theaters of world war 2 was most closely associated with the surrender of the Germans to the USA?

You don't give us the names of "these" theaters you have been given to chose from, so we can't tell. But the most important theaters of war in 1945 for the USA were Italy, France and Germany itself. The Germans by the way did not surrender to the USA; they surrendered to the combined Allied Powers: Great Britain, the USA, the Soviet Union and France.