You'd still stuck with the built environment as it is, just as everybody else.
A billion is just three Manhattan skyscrapers, so it can't change a city. Depending on where you live, you might well experience the exhaust, dust and noise of these environments, no matter how luxurious your individual dwelling.
I think that's more a problem with being famous: the top of the Wikipedia list* as I write this is "Bernard Arnault & family", who I've never heard of and therefore couldn't spot in a lineup much less a crowd.
But I did double-take when walking past Russell T Davis (or a lookalike) in Sheffield a decade and a half ago, and Richard Osman in Cambridge train station some other time.
A billion is just three Manhattan skyscrapers, so it can't change a city. Depending on where you live, you might well experience the exhaust, dust and noise of these environments, no matter how luxurious your individual dwelling.