Which neutral country was surrounded by axis conquests and axis countries?

Switzerland

Switzerland declared their neutrality in the war initially and quickly became surrounded by Axis powers. To the north Germany, east Austria, south Italy, and to the west an occupied France. 

Switzerland is a diverse country and the decision to be neutral was partially based on the split loyalties within the country. There are people of German descent as well as French who were enemies in the war. There are also Italian influences in Switzerland. The mountains of the country helped ensure their isolation.