'Or the best place I've ever lived?' Or maybe 'The best plave I've ever lived in?' I'm not sure, thanks.
Dropping the relative adverb or the relative pronoun with the preposition preceding it is possible after some common nouns only in colloquial English. See this explanation from page 498 of "Practical English Usage" by Swan:
However, it is grammatically more correct to say:
- the best place where I've lived
- the best place (that) I've lived in