It makes you sound like you have a good education but no one can tell quite where you are from. You hear it in old Hollywood films from the 1930s and 1940s. It is the accent of Cary Grant, Katherine Hepburn, William F Buckley and (at least in some films) God.
There is no town in the world where people grow up speaking English that way. Instead you get the accent in one of three ways:
1. Learn the accent on purpose (actors used to do that).
2. Grow up or live on both sides of the Atlantic (but that can lead to even stranger accents, like those of Loyd Grossman and Madonna).
3. Pick it up at a top boarding school in America before the 1960s.
Abagond has some tips to help you cultivate a Transatlantic accent. Link -via Cynical-C