a) "London is the best place to live."
b) "London is the best place to live in."
b) is very likely correct English. But I heard of a) being used liberally by native speakers. Is a) informal?
London is a great place to live.
Madrid was my favourite place to live.
Eastbourne is a very quiet place to live.
With types of accommodation, I would use the preposition.
A house is the best type of accommodation to live in.
A flat is a practical type of accommodation to live in.
A caravan would be cramped to live in.