Not to mention just the geography and circumstance of the area itself, apart from being where Obama actually lives: a racially integrated community area on the South Side of Chicago, home to Harold Washington while he was mayor, boasting one of the top universities in the world, where both Obamas formerly worked. It's pretty heavily intertwined with the narrative he's built for himself. I remember I was in Hyde Park on Election Night in 2008--it's hard to separate the man from that place.
The other three possibilities all lacked the resonance of the Hyde Park choice. So I guess this pick seems pretty obvious.