As others have said, going to the northern part. Depending on the state it usually carries with it the idea of a change of scenery abd culture.
For example a New Yorker may say “upstate” referring to the more rural areas.
Similar to how “out west” in early US history meant “wild and untamed country full of potential, opportunities and danger”
While I’ve never heard down state I have heard similar.
“Down south” or “below I10” or “Cajun country” in parts of Louisiana and Mississippi referring to the gulf, more Catholic Cajun areas. And down south in other states referring to the southern states.