If I returned to the U.S. from living overseas for two years, do I enter the date that I returned as the date that I established residency? Also does it affect my taxes?

@mfroiz , assuming that you are a US citizen/Resident ( Green Card ) whom have worked abroad for the last two years  and have  returned  home , then start of residency  for the State tax purposes  is generally  ruled by the State  laws . Often this is the date when you re-established  your  physical presence in the state.

I am not sure that this is what you meant -- so please explain in what context are you looking for the date  when you established  residency.   There seems to more  there in this question