Is the place [where the famous scientist was born] the one [(that/what) I mentioned to you last time]?

解析：句子为主系表结构，主语是 the place where the famous scientist was born，其中有一个关系副词 where 引导的定语从句，先行词为 place；表语是 the one I mentioned to you last time，其中有一个省略了的关系代词引导的定语从句，先行词为 one。

翻译：那个有名的科学家出生的地方是我上次跟你提到的那个地方吗？

Is the place where the famous scientist was born the one (that) I mentioned to you last time?

=Is the place in which the famous scientist was born the one (which) I mentioned to you last time?

参考译文：那个著名的科学家出生的地方是我上次跟你提起过的那个地方吗？

同意谭老师和曾老师解答

(1)关系副词where引导定语从句，where 在定语从句作地点状语，相当于in which

(2)关系代词that引导定语从句，that 在定语从句作mention的宾语成分，相当于which