a good friend of mine from----I was born showed up at my home before i left for beijing

应该是填where.但是不叫定语从句,而是宾语从句吧.a good friend of mine from = a good friend of mine（who comes）from,介词后面加宾语,who是主语 comes from是谓语动词.谓语动词后面一般紧跟着宾语.故此处应该是宾语从句才对吧.
the place where I was born=the place on which I was born 才是定语从句,而且此处的on不是想要就要不要就不要的,一定要记得加上啊.而where I was born是表示地点的.例如：Put the book where it was.把书放在它原来的地方.where it was这里的where it was 是地点状语.