Voting in the US

I know that, since I will still be a US Citizen, I will be entitled to vote in US elections when I will be living in the UK.

But I am registered as a resident of New York State.  I will no longer be living in New York State, so how does that work? I am planning to maintain an "in care of" address at a relative's home in New York, just so I can get mail in the US, but I don't want that counted as the address where I am living; I want my official residence to be in the UK, because of the foreign income tax exclusion.

You don't have to maintain an address in the US, you just vote (by post) in the state in which you were last resident.

Here is the link you will need.

http://www.usembassy.org.uk/cons_web/acs/scs/voting.htm

Where you vote "through" is based on your last residence in the US.