to 表示“来到；到达”（某地点或方位），into 表示“进入”（有空间或体积的事物）。例如：

get to the house：到达房子的位置。

get into the house：进入房内。

come to one's mind，是个习语。mind 表达抽象意义（人的意识），不表示空间或体积概念，没有内外界限，所以用to 就完全可以了。但实际语言中，人们使用into 的情况也很多，意思相同。例如：

An idea has just come into my mind. 我刚想到一个主意。

An image of a country garden came into my mind. 我脑子里浮现出一幅农村花园的景象。

A slight doubt came into my mind when I saw them. 当我看到他们时，我有一丝的怀疑。

An idea came into his mind suddenly. 他突然想到了一个主意。

One day, Gates found that people always used adding machines to summarize and classify the handwritten accounts then an idea came into his mind. 一天，比尔发现人们总是用加法机将手写的账目进行分类总结。

That was just an excuse. I wanted to get back early, and I said the first thing that came into my mind. 那仅是借口。我想早点回家，就慌不择言，想到什么就说了什么。

It came into my mind that Alan, on the day of that battle, had been engaged upon the royal side. 我想起了，战斗发生的那天，艾伦原是给国王那边当差的。

没有come in one's mind 的表达。