Scroll down on this page. You'll find a helpful guide to this capitalization question: Capitalization Rules - Rule for Capitalization Especially for ESL Students.
It's different for geographic divisions, however. There's a good guide at this webpage: Capitalization — FactMonster.com.
As far as the American states go, just ask yourself this: Is it part of the name? If it's not, then don't capitalize it.
Here's another example:
Capitalize "Southern" in Southern New Hampshire University, but don't capitalize "southern" in "southern New Hampshire".
southern New Hampshire - Google Search
Capitalize East Boston because this is the name of a section of Boston, but don't capitalize eastern Massachusetts, unless for some reason "eastern Massachusetts" is part of a title or a name, as in "Eastern Massachusetts Savings Bank".
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