你的句子不可以换成 that is why…，这里的 which 引导的是非限制性定语从句，关系代词 which 指代前的句子说的内容。若一定要换成 that，就应加上连词 and，使之构成并列句。如：

Rome can be pricey for travelers, and that is why many choose to stay in a hostel (旅社). The hostels in Rome offer a bed in a dorm room for around $25 a night, and for that, you’ll often get to stay in a central location (位置) with security and comfort.

再举几例。下面句子中的 which is why 也不能换成 that is why，但可以换成 and that is why：

Ice is less dense than water, which is why it floats. 冰的密度小于水，所以会浮在水上。

He was called away unexpectedly today, which is why I came to meet you instead. 他今天突然被叫走了，所以才换了我来见你。

I’m afraid he’s more of a talker than a doer, which is why he never finishes anything. 我觉得他说得多，做得少，这就是他始终一事无成的原因。