This is what you need to do.
1. Find an address that is in Connecticut but not in Fairfield County as that is part of the New York DMA. Best way of getting an address, from what I've found is find a neighborhood that has house addresses that skip (i.e. 12 Elm St then 15 Elm St., pick 13 or 14 Elm Street, where a house isn't sitting there.). You do not need relatives.
2. Pick paperless billing then you don't have to worry about bills going to a nonexistant address. Pay the bills online.
3. Call Directv and tell them you have moved, your equipment is installed already, and you just need the service address changed.
Before I saw your second question, I was gonna ask if you lived near the North Shore because normally North Shore residents can get WFSB, WTNH, and others on an antenna but since you have basic cable, there should be no problem and no reason to "move" your address back unless you have equipment issues. Most of New Haven County gets WNBC, WCBS, and WNYW as significantly viewed stations to go with the Hartford stations but they are only in Standard Def. And the eastern part of Connecticut is eligible to get the CBS stations out of Boston and Providence (WBZ and WPRI). This is good if you watch the NFL and would like to see a different NFL game every week if you don't have Sunday Ticket.
Here is a link to signifcantly viewed locals by zip code.
DIRECTV: Neighboring Local Channels