It’s a bit dependent on the context i think. On it’s own, ‘A place to live’ is correct.
If you were conversing and using the term ‘place’ to refer to specifically a house or an apartment (your dwelling), you could say for example: “I’m looking for a place to live in”, or “My place is great to live in”. That would be perfectly acceptable speech. That’s the only time i could think you would use such a statement.
More usually you would say liv-ing in. I’m living in a place called... or I live in a place called...
Hope that helps!