填 that 或which 或不填都是对的.
先行词the days,we spent together 是定语从句,其中spent是及物动词,是要带宾语的,但从句了没有,所以从句缺少宾语,又先行词是物,故可填that或which或不填,因为关系代词做宾语时,可以省略.