I believe the answer is: a place where he feels comfortable and accepted
The phrase 'fit in' is used to compare his position in life with a puzzle. For a puzzle to fit in, the board need to provide a correct size of the puzzle so the puzzle piece does not need to be changed or reshaped to be placed properly.
In his life, this can be translated to a place where he is comfortable and accepted for who he is without having to change any of his characteristics.