A friend told me years ago
How many years ago? What were her exact words?
She passed about a year ago and I was never notified about my inheritance. Now I found out she decided to donate it to a museum
You mean she donated it while she was alive?
she never told me she had made the change. I know people can change their minds, but I feel she should have informed me of that.
You're entitled to feel however you feel. However, subject to your answers to the questions above, I think most people would regard this as completely unreasonable.
Would suing the estate for breach of promise be a futile endeavor?
Yes. Here's why:
1. "Breach of promise" is not a recognized cause of action in any U.S. jurisdiction. Breach of
contract is a recognized cause of action, but you have not asserted that any contract existed between you and your friend.
2. You presumably have no evidence of what your friend told you beyond your testimony. Since your friend is dead, she cannot testify.
3. While you didn't mention the relevant state, the statute of limitations to sue an estate is typically very short. You said your friend died "about a year ago." If that means more than a year, then the time to sue has likely expired.