the place--interested me most was the Children's Palace.

which/that 是关系代词,在从句里充当主语,宾语,或表语
where 是关系副词,在从句做状语 且where = in/at/on/under + which
the place（__interested me most） was the Children's Palace
首先分析这个句子：打了括号的是一个定语从句,用来修饰the place
这个从句里面interested 是动词,那么前面缺少的是主语,所以用关系代词which /that
附加：
I like the place（where we spent our holiday last summer. ）
从句里we是主语,our holiday是宾语 ,也就是说从句里不缺主语,不缺宾语,所以不能用which/that