live is an intransitive verb, and it needs to be followed by in in order to be followed by a noun~

But in some sentences it can be used with or without in, as I'll explain next~

I think it is a wonderful place to live.

I

I think it is a wonderful place to live in.

These two sentences seem to be the same at first glance, with the infinitive as a determiner. However, there is a big difference.

Live in the first sentence means "to live", which is the state of the infinitive, so there is no need for a preposition.

A place to live could have been a fixed term

Live in the second sentence means "to live", and as a verb, it means to live in a building, so you need to add the preposition in.