place to live... or place to live in

[pseudo]

Hello everyone.

s1. It's a good house to live in.

I think that in s1 'in' must not be omitted.

s2. It's a good place to live in.

s3. It's a good place to live.

In this sense, s2 is correct but I sometimes see sentences like s3.
I think some nouns can be used like this.
But I don't know specifically what kind of nouns including place can be used like this.

s4. There are many good places to [go / go to]?

Which one is correct? If both are correct, under what circumstance can both be correct?

[Tdol]

s4. There are many good places to [go / go to]?

You could use either. There's no real difference.