James' answer covers the legalities pretty succinctly.
Technically, however, the POTUS could kick the UN Headquarters out of New York, by "simply" unilaterally withdrawing the US from any and all United Nations memberships and treaties -- at which point the US would no longer be bound by the UNHQ agreement and could tell them to piss off.
Of course, the diplomatic, political and economic cost of a move like that would be catastrophic, but if he really wanted to, he could.
What would be more likely to happen in practice would be that the US would formally ask the UN to move their headquarters elsewhere, and the UN would probably answer "Sure, just as soon as we agree on another country/city to host the HQ and finish building it" which would probably take quite a while.