This is a burning question. I'll put you out of your misery. The answer is: they both live in the Ritz Carlton Hotel in Downtown Manhattan right now.
We made our way down to the tip of Manhattan (yes, past the World Trade Center site, around the Stock Exchange, through Battery Park for a glimpse of the Statue of Liberty) and to Battery Park City. I hadn't known the distinction before, but check out the cool origins of Battery Park City:
By the 1950s, Manhattan found itself with a boatload (no pun intended) of "finger piers" adjacent to the Financial District in Lower Manhattan. These piers- and there were dozens of them- were outdated and pretty much useless because they were way too small to accomodate modern-day cargo ships. Not only were they not useful, they were becoming blighted, attracting crime, and generally starting to infect the valuable parts of the Financial District. On top of it all, the Financial District was lacking enough modern office space (the kind that could accomodate those new-fangled computers and such) and businesses were leaving the area altogether.
So by the 1960s, somebody (actually, it was businessman David Rockefeller, with the support of his then-NY-Governor-brother Nelson Rockefeller) got the bright idea to 1) build the World Trade Center complex of buildings and 2) use the considerable amount of excavated earth to 3) fill in the outmoded pier area. They literally dumped zillions of acres or pounds or whatever of dirt right onto the piers. In this way, the shape of Lower Manhattan was significantly altered and Battery Park City now stands on top of the old piers/on top of the dirt from the World Trade Center excavation (looks like a bulge on the left side of this map). COOL, huh?
As an aside, I think the developers of the WTC were supposed to pay a bunch of money into a fund to build affordable/subsidized housing in Battery Park City, but my quick research gives me the feeling that the rich guys didn't want The Projects anywhere near their fancy new skyscrapers, so the money went elsewhere. Today, BPC seems to be full of only high-end housing and beautiful jogging paths along the Hudson River overlooking New Jersey across the way.
As if Battery Park City isn't cool enough already, just by virtue of its "birth" as a landfill site atop the skeleton of the old 19th century pier complex, it also is the site of the Ritz Carlton Hotel, which happens to also house the very cool Skyscraper Museum. But when we showed up at the Ritz Carlton, we were greeted by literally a hundred security guards, dozens of NYPD vehicles, a Coast Guard ship stationed off shore. We practically had to get a cavity search to get within 100 yards of the Ritz (ok, not really, but it was pretty weird to have to go through full airport-style security on a public street). What gives, I innocently asked one of the gentlemen wearing an ill-fitting suit and talking into his sleeve periodically.
DUH!!! It is the big UN meeting in town and, of all people, Iranian President Mahmoud Ahmadinejad was staying at the Ritz, hence the crazy security action. Not only was he staying there, but they were having some sort of ball that Saturday night and by the time we left the museum around 6 pm, the tuxes and gowns were arriving en masse. Too funny to see so many very important people, dressed in their finest, be super pissed-off that they couldn't drive up to the hotel and that they had to go through the un-glamorous security process in their ultra-fancy clothes.
The next day, Sunday, we were walking past the Waldorf=Astoria (don't blame me for that stupid "double hyphen" on the name, that's the official spelling) near our own hotel in Midtown, and security was even crazier. Turns out, that's where President Bush was staying!