a) I found a new place to live.
b) I found a new place to live in.
Can you find the pattern?
live in a nice place
She is happy to have found such
a nice place to live (in).
in Cambridge
Cambridge is an attractive place, and quite an easy place to live in.
live in the world
The world will be a better place to live in.
live in Bali
Bali is a wonderful place to live in.
live in the world
Few care about making the world a better place to live in.
*in a place to live / live in a better place
It's a better place to live (in).
*in a place to live
It's hard to find a place to live quickly.
live in the USA
The USA is a wonderful place to live (in) and to study.
live in LA
Los Angeles is a pleasant place to live (in).
live in a new place / *in a new place to live
I found a new place to live (in), in West Ham.