The shortest description of me is a pair (U, x), where U is a description of my universe and x is a description of where to find me in that universe.

It might not be possible to describe U without making some arbitrary choices concerning "co-ordinates" (and other acts of "gauge-fixing"). And then when they're chosen, we're going to want to 'throw them away' once we've located the observer (since the co-ordinates are not physically meaningful and certainly don't form part of the observer's "mental state".)

So really, it's better to talk about a "centred universe" whose co-ordinates are specially chosen to have the observer in the middle, rather than an uncentered ("objective") universe plus a pointer.

Anyway, I still want to know whether being close to a 'landmark' (like a supermassive black hole) is going to significantly increase one's probability. And whether, if tons of copies of you are made and sent far and wide, you should 'anticipate' waking up close to a landmark.